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Removing DESpecs directory which deserted to git
| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Wed, 29 Nov 2017 16:55:37 +0100 |
| parents | 22d6a63640c6 |
| children |
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<?xml version="1.0" encoding="utf-8"?><echo xmlns="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:de="http://www.mpiwg-berlin.mpg.de/ns/de/1.0/" xmlns:dcterms="http://purl.org/dc/terms" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:echo="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:xhtml="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.0RC"> <metadata> <dcterms:identifier>ECHO:catan_belli_502_la_1600.xml</dcterms:identifier> <dcterms:creator identifier="GND:129226815">Cataneo, Girolamo</dcterms:creator> <dcterms:title xml:lang="la">De Arte Bellica</dcterms:title> <dcterms:date xsi:type="dcterms:W3CDTF">1600</dcterms:date> <dcterms:language xsi:type="dcterms:ISO639-3">lat</dcterms:language> <dcterms:rights>CC-BY-SA</dcterms:rights> <dcterms:license xlink:href="http://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA</dcterms:license> <dcterms:rightsHolder xlink:href="http://www.mpiwg-berlin.mpg.de">Max Planck Institute for the History of Science, Library</dcterms:rightsHolder> <echodir>/permanent/archimedes_repository/large/catan_belli_502_la_1600</echodir> <log>KT: erste Seite selber abgetippt (2010-10-19)</log> </metadata> <text xml:lang="la" type="free"> <div xml:id="echoid-div1" type="section" level="1" n="1"> <pb file="00001" n="1"/> <head xml:id="echoid-head1" xml:space="preserve">HIER.<lb/>CATANEVS</head> <head xml:id="echoid-head2" xml:space="preserve">DE ARTE BEL-<lb/>LICA,<lb/>*<lb/>SIVE, </head> <head xml:id="echoid-head3" style="it" xml:space="preserve">De deſignandis ac construendis acribus &<lb/>propugnaculis, nec non & de iis oppugnan-<lb/>dis, expugnandis, ac propugnandis: de iti-<lb/>nere exercitus, ac castrametione: quan-<lb/>do expediat manus cum hoste conſerere:<lb/> ac tandem, quid imperatori ſit in precin-<lb/>ctu cauendum vel eligendum.</head> <p> <s xml:id="echoid-s1" xml:space="preserve">Ex typographeo<lb/>IO. TORNÆSII LVGDVN<lb/>ⅭⅠↃ. ⅠↃ. Ⅽ.</s> </p> <pb file="00002" n="2"/> <pb file="00003" n="3"/> <figure> <image file="00003-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/00003-01"/> </figure> </div> <div xml:id="echoid-div2" type="section" level="1" n="2"> <head xml:id="echoid-head4" xml:space="preserve">Ad ampliſsimum, nobiliſsimúmq;</head> <head xml:id="echoid-head5" style="it" xml:space="preserve">virum, D. de Vic, Henrici IIII. Galliarum & <lb/>Nauarræ Regis Christianiſsimi, in ſacro conſiſto-<lb/>rio ſapientißimum Conſiliarium, ac in Senatu <lb/>Toloſano Præſidem integerrimum, & c.</head> <p> <s xml:id="echoid-s2" xml:space="preserve"><emph style="sc">TAntvm</emph> ſcit quiſque quantum fa-<lb/>cit, dicebat quidam ex patribus: </s> <s xml:id="echoid-s3" xml:space="preserve">idq́; <lb/></s> <s xml:id="echoid-s4" xml:space="preserve">commodè. </s> <s xml:id="echoid-s5" xml:space="preserve">Inutiles enim, V.</s> <s xml:id="echoid-s6" xml:space="preserve">A. </s> <s xml:id="echoid-s7" xml:space="preserve">vi-<lb/>dentur ſcientiæ, quales quales ſint, <lb/>niſi fructus aliquis ex eis in publicum manet: </s> <s xml:id="echoid-s8" xml:space="preserve">nec <lb/>etiam nobis ſolùm nati ſumus, quod eſt apud e-<lb/>loquentiæ parentem: </s> <s xml:id="echoid-s9" xml:space="preserve">verùm ortus noſtri partem <lb/>patria ſibi vendicat, partem amici. </s> <s xml:id="echoid-s10" xml:space="preserve">Qui ſibi tan-<lb/>tummodo docti ſunt, ij etiam ſibi ſolùm nati. </s> <s xml:id="echoid-s11" xml:space="preserve"><lb/>Sunt itaque maxima laude digni, qui omnia ſua <lb/>ſtudia, omnes ſuas actiones, ad publicam vtilita-<lb/>tem referunt. </s> <s xml:id="echoid-s12" xml:space="preserve">In quorum album, V.</s> <s xml:id="echoid-s13" xml:space="preserve">A. </s> <s xml:id="echoid-s14" xml:space="preserve">referendus <lb/>es, ſi quiſquam alius. </s> <s xml:id="echoid-s15" xml:space="preserve">Quum enim diuina cle-<lb/>mentia te omnigenis dotibus cumularit, inte-<lb/>grum ex iis fructum publico donas. </s> <s xml:id="echoid-s16" xml:space="preserve">Adde quòd, <lb/>præter alias ſcientias, politicam præcipuè elegi-<lb/>ſti, ad quam reliquas omnes referres. </s> <s xml:id="echoid-s17" xml:space="preserve">τ @ πολι<unsure/>η<unsure/>-<lb/>κῆς {αὔ}{θρ}ωπ{ος} {ἀρ}ετῆς οὐ κτᾶ@ τελ@οτέ{ρα}ν, ait hiſtori- <pb file="00004" n="4"/> cus Chæronenſis. </s> <s xml:id="echoid-s18" xml:space="preserve">Hæc in cauſa ſunt cur Rex <lb/>Chriſtianiſſimus te ſibi adeſſe à conſiliis volue-<lb/>rit, tibiq́; </s> <s xml:id="echoid-s19" xml:space="preserve">quotidie præcipua regni negotia com-<lb/>mittat. </s> <s xml:id="echoid-s20" xml:space="preserve">Deus bone, qualis Rex! Rex veré ad re-<lb/>gnum natus, cui licet ſagax ſit ingenium, pru-<lb/>dentia admiranda, judicium firmum, fortitudo <lb/>inexpugnabilis, nihilominus ſuorum lubenter <lb/>audit conſilia, & </s> <s xml:id="echoid-s21" xml:space="preserve">in iis acquieſcit, vbi videt ex re <lb/>ſuâ eſſe: </s> <s xml:id="echoid-s22" xml:space="preserve">rem autem ſuam eſſe cenſet rem publi-<lb/>cam, rem regni. </s> <s xml:id="echoid-s23" xml:space="preserve">Beatiſſimum quidem in Princi-<lb/>pe non cogi: </s> <s xml:id="echoid-s24" xml:space="preserve">miſerrimum verò non perſuaderi: <lb/></s> <s xml:id="echoid-s25" xml:space="preserve">aſt beatiſſimum regnum, cujus Princeps ſanis ſa-<lb/>narum mentium conſiliis aurem præbet. </s> <s xml:id="echoid-s26" xml:space="preserve">Verùm <lb/>de his, prout deceret, diſſerere, mearum non eſt <lb/>virium. </s> <s xml:id="echoid-s27" xml:space="preserve">Aliis ergo hoc immenſum pelagus ena-<lb/>uigandum relinquo. </s> <s xml:id="echoid-s28" xml:space="preserve">De noſtro hoc libello jam <lb/>à me pauxillus fiet ſermo. </s> <s xml:id="echoid-s29" xml:space="preserve">Multi multa de arte <lb/>militari, variis temporibus, variis linguis, varia <lb/>methodo. </s> <s xml:id="echoid-s30" xml:space="preserve">Fateor. </s> <s xml:id="echoid-s31" xml:space="preserve">Sed, ni fallor, pauci qui tan-<lb/>ta facilitate, tam exactè, tam ex vſu noſtro, quàm <lb/>noſter hic Cataneus. </s> <s xml:id="echoid-s32" xml:space="preserve">Id in cauſa fuit, cur ſemel <lb/>atq; </s> <s xml:id="echoid-s33" xml:space="preserve">iterum hunc noſtrum auctorem aliter quàm <lb/>Italicè loqui docuerim: </s> <s xml:id="echoid-s34" xml:space="preserve">primò Gallicè, nunc ve-<lb/>rò Latinè. </s> <s xml:id="echoid-s35" xml:space="preserve">Hanc autem meam interpretationem <lb/>Latinam cui potiùs, quàm tibi, offerrem non vi-<lb/>di. </s> <s xml:id="echoid-s36" xml:space="preserve">Eam ergo, V.</s> <s xml:id="echoid-s37" xml:space="preserve">A. </s> <s xml:id="echoid-s38" xml:space="preserve">tibi do, dicoq́;</s> <s xml:id="echoid-s39" xml:space="preserve">: petoq́; </s> <s xml:id="echoid-s40" xml:space="preserve">abs <lb/>te, vt hanc meam in te obſeruantiam boni con-<lb/>ſulas. </s> <s xml:id="echoid-s41" xml:space="preserve">At, dicet aliquis, quid {α\’ν}{δρ}ὶ πολ{ιμ}κω{τά}τω <pb file="00005" n="5"/> cum Marte & </s> <s xml:id="echoid-s42" xml:space="preserve">Bellona? </s> <s xml:id="echoid-s43" xml:space="preserve">Quite non norunt, ita <lb/>forſan loquentur: </s> <s xml:id="echoid-s44" xml:space="preserve">aſt ij, quibus penitiùs innotui-<lb/>ſti, aliter ſentient. </s> <s xml:id="echoid-s45" xml:space="preserve">Pacis artibus clarus es: </s> <s xml:id="echoid-s46" xml:space="preserve">omnes <lb/>fatentur. </s> <s xml:id="echoid-s47" xml:space="preserve">aſt bellicarum non ignarus: </s> <s xml:id="echoid-s48" xml:space="preserve">immò pe-<lb/>ritiſſimus. </s> <s xml:id="echoid-s49" xml:space="preserve">quod patuit ex ſumma illa diligentia <lb/>& </s> <s xml:id="echoid-s50" xml:space="preserve">ſedulitate, quâ vſus es in extremis Gallorum <lb/>bellis ciuilibus: </s> <s xml:id="echoid-s51" xml:space="preserve">præcipuè dum attentè & </s> <s xml:id="echoid-s52" xml:space="preserve">ad a-<lb/>muſſim obſeruas ac recognoſcis ciuitates & </s> <s xml:id="echoid-s53" xml:space="preserve">ar-<lb/>ces, quæ à perduellibus occupabantur, earumq́; <lb/></s> <s xml:id="echoid-s54" xml:space="preserve">ſitum, aditus, loca firma, loca infirma perluſtras. </s> <s xml:id="echoid-s55" xml:space="preserve"><lb/>Verùm, in commoda publica peccem, ſite, gra-<lb/>uioribus rebus occupatum, in hujus epiſtolæ le-<lb/>ctione diutiùs detineam. </s> <s xml:id="echoid-s56" xml:space="preserve">Finem igitur faciam, <lb/>poſtquam iterum à te, V.</s> <s xml:id="echoid-s57" xml:space="preserve">A. </s> <s xml:id="echoid-s58" xml:space="preserve">petiero, vt hanc <lb/>meam dicationem æqui boniq́; </s> <s xml:id="echoid-s59" xml:space="preserve">conſulas.</s> <s xml:id="echoid-s60" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s61" xml:space="preserve">D.</s> <s xml:id="echoid-s62" xml:space="preserve">O.</s> <s xml:id="echoid-s63" xml:space="preserve">M. </s> <s xml:id="echoid-s64" xml:space="preserve">te diu Galliarum Regi regnoq́; </s> <s xml:id="echoid-s65" xml:space="preserve">in-<lb/>columem ſeruet. </s> <s xml:id="echoid-s66" xml:space="preserve">Exmuſæo noſtro a. </s> <s xml:id="echoid-s67" xml:space="preserve">d. </s> <s xml:id="echoid-s68" xml:space="preserve">7 Id. <lb/></s> <s xml:id="echoid-s69" xml:space="preserve">Apr. </s> <s xml:id="echoid-s70" xml:space="preserve">anno à virgineo partu CIC<unsure/>. </s> <s xml:id="echoid-s71" xml:space="preserve">IC<unsure/>. </s> <s xml:id="echoid-s72" xml:space="preserve">C.</s> <s xml:id="echoid-s73" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s74" xml:space="preserve">T. </s> <s xml:id="echoid-s75" xml:space="preserve">A. </s> <s xml:id="echoid-s76" xml:space="preserve">ſeruus addictißimus <lb/>foannes Tornæſius.</s> <s xml:id="echoid-s77" xml:space="preserve"/> </p> <figure> <image file="00005-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/00005-01"/> </figure> <p style="it"> <s xml:id="echoid-s78" xml:space="preserve">Quadrans, ſeu quarta pars pedis communis Venetiani, ſeu Veronenſis, qua <lb/>menſura vſus eſt auctor in hoc opere.</s> <s xml:id="echoid-s79" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s80" xml:space="preserve">Quadrans brachy Brixiani.</s> <s xml:id="echoid-s81" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s82" xml:space="preserve">Quadrans pedis antiqui.</s> <s xml:id="echoid-s83" xml:space="preserve"/> </p> <pb file="00006" n="6"/> <figure> <image file="00006-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/00006-01"/> </figure> </div> <div xml:id="echoid-div3" type="section" level="1" n="3"> <head xml:id="echoid-head6" xml:space="preserve">PROLEGOMENA QVÆDAM HIER. <lb/>Catanei in opus ſuum.</head> <figure> <image file="00006-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/00006-02"/> </figure> <p style="it"> <s xml:id="echoid-s84" xml:space="preserve">_<emph style="sc">MInime</emph>_ dubium eſt, quin munitiones ciuita-<lb/>tum ac caſtellorum præcipuum locum obtineant <lb/>inter ea, quæ à Principibus fiunt ad ſuas terras <lb/>conſeruandas: </s> <s xml:id="echoid-s85" xml:space="preserve">ditionis enim ipſorum ſalus, nec-<lb/>non & </s> <s xml:id="echoid-s86" xml:space="preserve">totius populi, ab illis maxima ex parte <lb/>pendet. </s> <s xml:id="echoid-s87" xml:space="preserve">Quamuis autem multa circa eas conſiderari debeant, <lb/>nihilominus, pro captu meo, ac pro vſu, quem mihi ſuppedita-<lb/>runt, tum Mathematicæ diſciplinæ, tum etiam experientia, <lb/>quam per multos annos acquiſiui, ſigillatim, vt potero, de ys lo-<lb/>quar. </s> <s xml:id="echoid-s88" xml:space="preserve">Non tamen immorabor in recenſendis multis, quæ ad <lb/>ciuitatum ædificationem pertinent, vt ſunt aëris boni electio, <lb/>aquarum, terræ, & </s> <s xml:id="echoid-s89" xml:space="preserve">alia idgenus. </s> <s xml:id="echoid-s90" xml:space="preserve">Hæc enim à multis tam co-<lb/>piosè tractata ſunt, vt mihi ſuperfluum videretur de ys diſſere-<lb/>re, præcipuè quum instituerim agere tantùm de munitionibus, <lb/>& </s> <s xml:id="echoid-s91" xml:space="preserve">de qualitate machinarum quæ ys inſeruiunt, prout fert no-<lb/>ſtrorum temporum vſus. </s> <s xml:id="echoid-s92" xml:space="preserve">Dico igitur eum, qui in animo ha-<lb/>bet munire ciuitatem, aliúmve locum, debere primùm habere <lb/>ſitus rationem, præcipuè vbi munitiones illæ fiunt in limite ſuæ <lb/>ditionis. </s> <s xml:id="echoid-s93" xml:space="preserve">Quum enim loca illa limitanea ad id potißimùm con-<lb/>ſtruantur, vt facilè poßint injuriam & </s> <s xml:id="echoid-s94" xml:space="preserve">repellere & </s> <s xml:id="echoid-s95" xml:space="preserve">inferre, de-<lb/>bent ita parari, vt, minimo cum labore, annona, & </s> <s xml:id="echoid-s96" xml:space="preserve">alia neceſſa-<lb/>ria poßint inferri, & </s> <s xml:id="echoid-s97" xml:space="preserve">milites præſidiary ac ſubſidiary introduci. <lb/></s> <s xml:id="echoid-s98" xml:space="preserve">Præterea debent eſſe ejus capacitatis, vt, prout caſus belli feret, <lb/>præter præſidium ordinarium, poßint etiam illic eſſe & </s> <s xml:id="echoid-s99" xml:space="preserve">equites <lb/>& </s> <s xml:id="echoid-s100" xml:space="preserve">pedites, ad eruptiones & </s> <s xml:id="echoid-s101" xml:space="preserve">velitationes faciendas, ad agendas <pb file="00007" n="7"/> prædas, & </s> <s xml:id="echoid-s102" xml:space="preserve">alia id genus quæ quotidie occurrunt. </s> <s xml:id="echoid-s103" xml:space="preserve">Videndum <lb/>tamen erit, ne magnitudo locitanta ſit, vt Principem opprimat <lb/>ſumptus, tum in milites, tum in commeatum neceſſarium. </s> <s xml:id="echoid-s104" xml:space="preserve">Non <lb/>debet etiam tam exiguus eligi locus, vt tandem, ſed ſeriùs quàm <lb/>par eſſet, agnoſcatur, paucißimi, vel potiùs nullius vſus eſſe. <lb/></s> <s xml:id="echoid-s105" xml:space="preserve">Debet igitur ea electio fieri, maturè priùs perpenſis, tum facul-<lb/>tatibus ipſius Principis, tum etiam commoditatibus ac neceßi-<lb/>tate ipſius munitionis. </s> <s xml:id="echoid-s106" xml:space="preserve">Verùm, in tali electione, debemus præ-<lb/>cipuè ejicere animum ab ys omnibus, in quibus ſitus commodus, <lb/>vel alia opportunitas deficit, quamvis ſint amplæ ciuitates, <lb/>vel magna castella. </s> <s xml:id="echoid-s107" xml:space="preserve">Sæpe enim vidimus magnos ſumptus im-<lb/>penſos eſſe in munitiones ſimilium locorum abſque vllo fructu. </s> <s xml:id="echoid-s108" xml:space="preserve"><lb/>Quòd ſi mihi fides habeatur, multo ſatius eſſet, vel omnino no-<lb/>uas munitiones facere, velnouos aggeres exſtruere in loco op-<lb/>portuno, ad conſeruanda loca illa incommoda, & </s> <s xml:id="echoid-s109" xml:space="preserve">periculi non <lb/>expertia, quæ, etiam ſi bene ſita eſſent, nihilominus, propter <lb/>ipſorum vastitatem, ſeſe tueri non poſſent, niſi cum immenſo <lb/>ſumptu. </s> <s xml:id="echoid-s110" xml:space="preserve">Iterum igitur dico, maturè hæc perpendi debere. </s> <s xml:id="echoid-s111" xml:space="preserve">Hoc <lb/>autem, multorum judicio, non fuit à Senenſibus obſeruatum, <lb/>anno 1554, in munitione portus Herculani: </s> <s xml:id="echoid-s112" xml:space="preserve">dum enim ex hac <lb/>re fructum hunc cupiunt percipere, vt portus & </s> <s xml:id="echoid-s113" xml:space="preserve">ſe, & </s> <s xml:id="echoid-s114" xml:space="preserve">Senenſes <lb/>ipſos tueri poſſet, tandem innotuit, pleroſque aggeres incaſſum <lb/>factos fuiſſe: </s> <s xml:id="echoid-s115" xml:space="preserve">id́ hanc ob rem, quòd quum malè hæc munitio <lb/>fuiſſet deſignata, accidit vt breui, vno aggere amiſſo, reliqui o-<lb/>mnes, ſine mora, etiam in potestatem hostium venerint. </s> <s xml:id="echoid-s116" xml:space="preserve">Quem <lb/>caſum etiam ſubyt Bononia ad mare anno 1544, quum eſſent <lb/>circa eam quædam propugnacula erecta à rege Anglo, non ſo-<lb/>lùm malè ſita, ſed etiam infirma, quæ à Franciſco primo, Gal-<lb/>liarum rege, intra viginti dies expugnata fuerunt, &</s> <s xml:id="echoid-s117" xml:space="preserve">, ſine vllo <lb/>ferè labore, ſolo æquata. </s> <s xml:id="echoid-s118" xml:space="preserve">Negligere etiam non debet Princeps, <lb/>ad firmiorem ſuæ ditionis tuitionem, crebram recognitionem <pb file="00008" n="8"/> ſuarum munitionum: </s> <s xml:id="echoid-s119" xml:space="preserve">vt, quum diligentißimè perpenderit, quæ <lb/>earum conſeruari debeant, quæ autem derelinqui, has aperiat, <lb/>& </s> <s xml:id="echoid-s120" xml:space="preserve">muris nudet, illas verò fortiores, ac, quantum fieri poßit, in-<lb/>expugnabiles reddat: </s> <s xml:id="echoid-s121" xml:space="preserve">quod in Pedemonte fecit Princeps Mel-<lb/>py, Christianißimæ Majestatis Legatus, judicio ac conſilio va-<lb/>lens ſupra pleroſque alios duces: </s> <s xml:id="echoid-s122" xml:space="preserve">quum enim hac via procede-<lb/>ret, conatus, qui eo tempore, ac in ea regione, feliciter ſucceſſe-<lb/>runt, ac cum magna certitudine ad finem perducti ſunt. </s> <s xml:id="echoid-s123" xml:space="preserve">Di-<lb/>uerſum prorſus exitum vidimus in bello Senenſi. </s> <s xml:id="echoid-s124" xml:space="preserve">Quum enim <lb/>ex commiſeratione quædam castella, & </s> <s xml:id="echoid-s125" xml:space="preserve">alia loca, nec ſatis fir-<lb/>ma, nec omnino infirma, integra relicta eſſent inhabit antium <lb/>tutelæ, illuć accolæ vicini conduxiſſent facultates ſuas, tan-<lb/>dem & </s> <s xml:id="echoid-s126" xml:space="preserve">arces, & </s> <s xml:id="echoid-s127" xml:space="preserve">qui eas tutabantur, in manus hostium vene-<lb/>runt, prædǽ illis fuerunt: </s> <s xml:id="echoid-s128" xml:space="preserve">id́ maximo eorum damno: </s> <s xml:id="echoid-s129" xml:space="preserve">non <lb/>ſolùm enim accolæ commeatu ſuo orbati ſunt, ſed & </s> <s xml:id="echoid-s130" xml:space="preserve">hostium <lb/>exercitus eo ſubleuatus eſt. </s> <s xml:id="echoid-s131" xml:space="preserve">Unde accidit, vt & </s> <s xml:id="echoid-s132" xml:space="preserve">ciuitas & </s> <s xml:id="echoid-s133" xml:space="preserve">ciues, <lb/>cum capitis & </s> <s xml:id="echoid-s134" xml:space="preserve">vitæ periculo, (quam plerique omnes amitte-<lb/>bant) in manus hostium venirent. </s> <s xml:id="echoid-s135" xml:space="preserve">Præterea, quum arces ac <lb/>propugnacula ſint ad id præcipuè constructa, vt obſidionem ſu-<lb/>ſtinere poßint, eò debet intromitti commeatus, tum ad victum, <lb/>tum etiam ad alias res neceſſarias, id́ ad multo longius tem-<lb/>pus quàm par ſit, ne Princeps cogatur, ante finem belli, exer-<lb/>citum justum conſcribere ad ſuppetias obſeßis ferendum. </s> <s xml:id="echoid-s136" xml:space="preserve">Hæc <lb/>autem prolegomena, ſeu conſilia, viſum eſt hic à me ſcribi de-<lb/>bere, vt cum majori facilitate lectores poßint legen-<lb/>do percipere ea quæ in hoc opere tracta-<lb/>turus ſum de ichnographia ac <lb/>ſtructura propugna-<lb/>culorum.</s> <s xml:id="echoid-s137" xml:space="preserve"/> </p> <pb o="1" file="0001" n="9"/> <figure> <image file="0001-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0001-01"/> </figure> </div> <div xml:id="echoid-div4" type="section" level="1" n="4"> <head xml:id="echoid-head7" xml:space="preserve">Geometricæ quædam operationes, <lb/>quæ faciunt ad arcium ſeu pro-<lb/>pugnaculorum fabricam.</head> <head xml:id="echoid-head8" xml:space="preserve">CAPVT PRIMVM.</head> <p> <s xml:id="echoid-s138" xml:space="preserve"><emph style="sc">QVvm</emph> inſtituerim docere modũ <lb/>delineandi ac conſtruendi pro-<lb/>pugnacula, necnon & </s> <s xml:id="echoid-s139" xml:space="preserve">caſtrame-<lb/>tandi, aliaq́; </s> <s xml:id="echoid-s140" xml:space="preserve">peragendi quæ ad ar-<lb/>tem militarem pertinent: </s> <s xml:id="echoid-s141" xml:space="preserve">in qui-<lb/>bus docendis occurrit vt qua-<lb/>rumdam geometricarum ope-<lb/>rationum ſit vſus creberrimus: </s> <s xml:id="echoid-s142" xml:space="preserve">quàm breuiſſimè fieri <lb/>poterit eas explicabo, quæ mihi magis neceſſariæ vide-<lb/>buntur.</s> <s xml:id="echoid-s143" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div5" type="section" level="1" n="5"> <head xml:id="echoid-head9" xml:space="preserve">OPERATIO PRIMA.</head> <p> <s xml:id="echoid-s144" xml:space="preserve"><emph style="sc">Data</emph> linea recta, & </s> <s xml:id="echoid-s145" xml:space="preserve">in ea puncto, abeo <lb/>puncto deſcribere angulum rectilineum æ-<lb/>qualem angulo rectilineo dato.</s> <s xml:id="echoid-s146" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s147" xml:space="preserve">Sit linea <emph style="sc">AB</emph>, & </s> <s xml:id="echoid-s148" xml:space="preserve">in ea punctum <emph style="sc">C</emph>: </s> <s xml:id="echoid-s149" xml:space="preserve">angulus autem re-<lb/>ctilineus datus ſit <emph style="sc">DEF</emph>. </s> <s xml:id="echoid-s150" xml:space="preserve">Circini pedem figo in puncto <lb/><emph style="sc">E</emph> anguli <emph style="sc">DEF</emph>, & </s> <s xml:id="echoid-s151" xml:space="preserve">cum altero pede deſcribo circuli por-<lb/>tionem ſupra angulum <emph style="sc">DEF</emph>, quæ erit arcus <emph style="sc">GH</emph>: </s> <s xml:id="echoid-s152" xml:space="preserve">& </s> <s xml:id="echoid-s153" xml:space="preserve">cum <lb/>eadem circini apertura, figendo pedem immobilem in <lb/>puncto c, alterius pedis ope deſcribo arcum <emph style="sc">IK</emph> ſupra <pb o="2" file="0002" n="10" rhead=""/> lineam <emph style="sc">AB</emph>, & </s> <s xml:id="echoid-s154" xml:space="preserve">ab arcu <emph style="sc">IK</emph> detraho arcum æqualem ar-<lb/>cui <emph style="sc">GH</emph>, qui quidem erit arcus <emph style="sc">IL</emph>: </s> <s xml:id="echoid-s155" xml:space="preserve">deinde à puncto <emph style="sc">C</emph> ad <lb/>pũctum <emph style="sc">L</emph> duco lineam rectam <emph style="sc">CL</emph>, ſicq́; </s> <s xml:id="echoid-s156" xml:space="preserve">angulus <emph style="sc">LCA</emph> <lb/>angulo <emph style="sc">DEF</emph> erit æqualis: </s> <s xml:id="echoid-s157" xml:space="preserve">quod faciendum fuit. </s> <s xml:id="echoid-s158" xml:space="preserve">Hoc <lb/>autem docet Euclides vigeſima tertia primi, apparetq́; <lb/></s> <s xml:id="echoid-s159" xml:space="preserve">ex ſequenti figura.</s> <s xml:id="echoid-s160" xml:space="preserve"/> </p> <figure> <image file="0002-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0002-01"/> </figure> <p> <s xml:id="echoid-s161" xml:space="preserve">Quòd ſi angulo rectilineo dato æqualis angulus re <lb/>ctilineus deſcribendus eſſet ſuper puncto dato in li- <pb o="3" file="0003" n="11" rhead=""/> nea: </s> <s xml:id="echoid-s162" xml:space="preserve">deberetq́; </s> <s xml:id="echoid-s163" xml:space="preserve">ita deſcribi angulus ille rectilineus, vt <lb/>ejus dimidium eſſet ab vna parte dictæ lineæ, dimi-<lb/>dium verò ab altera, ita procedendum erit.</s> <s xml:id="echoid-s164" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s165" xml:space="preserve">Sit linea data <emph style="sc">AB</emph>: </s> <s xml:id="echoid-s166" xml:space="preserve">punctum verò in ea datum ſit <emph style="sc">C</emph>: <lb/></s> <s xml:id="echoid-s167" xml:space="preserve">angulus autem rectilineus datus, ſit <emph style="sc">DEF</emph>. </s> <s xml:id="echoid-s168" xml:space="preserve">Pedem cir-<lb/>cini immobilem figo in puncto <emph style="sc">C</emph>, cumq́; </s> <s xml:id="echoid-s169" xml:space="preserve">altero pede <lb/>portionem circuli deſcribo, quæ ſit <emph style="sc">PQ</emph>, qui arcus <emph style="sc">PQ</emph> <lb/>lineam <emph style="sc">AB</emph> ſecabit in puncto <emph style="sc">M</emph>. </s> <s xml:id="echoid-s170" xml:space="preserve">Iam, cum eadem cir-<lb/>cini apertura, deſcribo arcum ſuper angulo <emph style="sc">DEF</emph>, pe-<lb/> <anchor type="figure" xlink:label="fig-0003-01a" xlink:href="fig-0003-01"/> <pb o="4" file="0004" n="12" rhead=""/> dem immobilem figens in puncto <emph style="sc">E</emph>, eritq́; </s> <s xml:id="echoid-s171" xml:space="preserve">is arcus <lb/><emph style="sc">GH</emph>. </s> <s xml:id="echoid-s172" xml:space="preserve">Quo facto, diuido arcum <emph style="sc">GH</emph> in duas partes <lb/>æquales in puncto <emph style="sc">I</emph>. </s> <s xml:id="echoid-s173" xml:space="preserve">Deinde à duobus arcubus <emph style="sc">MQ</emph> & </s> <s xml:id="echoid-s174" xml:space="preserve"><lb/><emph style="sc">MP</emph>, detraho duos arcus, qui ſint arcubus <emph style="sc">IG</emph> & </s> <s xml:id="echoid-s175" xml:space="preserve"><emph style="sc">IH</emph> <lb/>æquales, eruntq́; </s> <s xml:id="echoid-s176" xml:space="preserve">ij arcus <emph style="sc">MN</emph>, & </s> <s xml:id="echoid-s177" xml:space="preserve"><emph style="sc">MO</emph>. </s> <s xml:id="echoid-s178" xml:space="preserve">Præterea à pun-<lb/>cto <emph style="sc">C</emph> ad duo puncta <emph style="sc">N</emph> & </s> <s xml:id="echoid-s179" xml:space="preserve"><emph style="sc">O</emph>, duco duas lineas rectas, <lb/><emph style="sc">CR</emph> & </s> <s xml:id="echoid-s180" xml:space="preserve"><emph style="sc">CS</emph>. </s> <s xml:id="echoid-s181" xml:space="preserve">Atq; </s> <s xml:id="echoid-s182" xml:space="preserve">ita prodibit angulus rectilineus, <emph style="sc">RCS</emph>, <lb/>angulo <emph style="sc">DEF</emph> æqualis, cujus dimidium erit ab vna par-<lb/>te lineæ <emph style="sc">AB</emph>, dimidium verò ab altera, quod facere in-<lb/>ſtitueramus, vt apparet in præcedenti figura.</s> <s xml:id="echoid-s183" xml:space="preserve"/> </p> <div xml:id="echoid-div5" type="float" level="2" n="1"> <figure xlink:label="fig-0003-01" xlink:href="fig-0003-01a"> <image file="0003-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0003-01"/> </figure> </div> </div> <div xml:id="echoid-div7" type="section" level="1" n="6"> <head xml:id="echoid-head10" xml:space="preserve">OPERATIO II.</head> <p> <s xml:id="echoid-s184" xml:space="preserve"><emph style="sc">Data</emph> linea recta, in eaq́; </s> <s xml:id="echoid-s185" xml:space="preserve">puncto dato, ab <lb/>eo puncto ducere lineam ad angulos rectos.</s> <s xml:id="echoid-s186" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s187" xml:space="preserve">Sit linea <emph style="sc">AB</emph>, in eaq́; </s> <s xml:id="echoid-s188" xml:space="preserve">punctum datum <emph style="sc">C</emph>, à quo pun-<lb/>cto ducenda ſit linea ad angulos rectos, quod ab aliis <lb/>dicitur ad perpendiculum, ſeu ad normam. </s> <s xml:id="echoid-s189" xml:space="preserve">Pedem <lb/>circini immobilem figo in puncto <emph style="sc">C</emph>, alterum verò pe-<lb/>dem extendo ad punctum <emph style="sc">B</emph>, vel ad aliud quoduis pũ-<lb/>ctum, quod ſit à parte <emph style="sc">B</emph>: </s> <s xml:id="echoid-s190" xml:space="preserve">cumq́; </s> <s xml:id="echoid-s191" xml:space="preserve">eadem circini apertu-<lb/>ra notabimus punctum in linea <emph style="sc">CA</emph>, non mouendo <lb/>pedem immobilem à puncto <emph style="sc">C</emph>: </s> <s xml:id="echoid-s192" xml:space="preserve">eritq́; </s> <s xml:id="echoid-s193" xml:space="preserve">punctum id <emph style="sc">D</emph>. <lb/></s> <s xml:id="echoid-s194" xml:space="preserve">Hoc facto pono pedem circini immobilem in puncto <lb/><emph style="sc">B</emph>, cumq́; </s> <s xml:id="echoid-s195" xml:space="preserve">pede mobili deſcribo lineolam <emph style="sc">E</emph> ſupra lineã <lb/><emph style="sc">AB</emph> : </s> <s xml:id="echoid-s196" xml:space="preserve">deinde, cum eadem circini apertura, figens pedem <lb/>immobilem in pũcto <emph style="sc">D</emph>, deſcribo aliam lineolam, quæ <lb/>priorem ſecet in puncto <emph style="sc">F</emph>. </s> <s xml:id="echoid-s197" xml:space="preserve">Iam ab interſectionis pun-<lb/>cto ad punctum <emph style="sc">C</emph> duco lineam rectam <emph style="sc">FC</emph>, quam di-<lb/>co ductam eſſe ad angulos rectos à puncto <emph style="sc">C</emph>, vt docet <lb/>Euclides vndecima primi propoſitione, proutq́; </s> <s xml:id="echoid-s198" xml:space="preserve">hîc in <pb o="5" file="0005" n="13" rhead=""/> proxima figura apparet.</s> <s xml:id="echoid-s199" xml:space="preserve"/> </p> <figure> <image file="0005-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0005-01"/> </figure> <p> <s xml:id="echoid-s200" xml:space="preserve">Quòd ſi punctum in linea datum propinquum eſ-<lb/>ſet alterutri lineæ extremitati, vel in ipſa extremitate, <lb/>producemus dictam lineam, deinde procedemus vt <lb/>ſuprà. </s> <s xml:id="echoid-s201" xml:space="preserve">Verùm ſi linea ita ſita ſit, vt nequeat produci, <lb/>hoc pacto operabimur: </s> <s xml:id="echoid-s202" xml:space="preserve">Figemus circini pedem im-<lb/>mobilem in puncto <emph style="sc">A</emph>, quod nobis datum eſt in extre-<lb/>mitate dictæ lineæ, cumq́; </s> <s xml:id="echoid-s203" xml:space="preserve">altero pede ſecabimus li-<lb/>neam in linea <emph style="sc">AB</emph>, quæ erit linea <emph style="sc">AC</emph>, ſupra quam <emph style="sc">AC</emph> <lb/>deſcribemus triangulum æquilaterum <emph style="sc">ADC</emph>, vt docet <lb/>prima primi Euclidis Propoſitio. </s> <s xml:id="echoid-s204" xml:space="preserve">Deinde producemus-<lb/>latus <emph style="sc">CD</emph>, aduſque punctum <emph style="sc">E</emph>, ita vt pars exterior pro-<lb/>ducta <emph style="sc">DE</emph> ęqualis ſit lateri <emph style="sc">DC</emph>. </s> <s xml:id="echoid-s205" xml:space="preserve">Iam à puncto <emph style="sc">A</emph> ad pun-<lb/>ctum <emph style="sc">E</emph> duco lineam rectam <emph style="sc">AE</emph>, quam dico produ-<lb/>ctam eſſe ad angulos rectos à puncto <emph style="sc">A</emph> dato in linea <lb/><emph style="sc">AB</emph>, vt videre eſt in ſequenti figura, quodq́; </s> <s xml:id="echoid-s206" xml:space="preserve">faciendum <lb/>ſuſceperamus.</s> <s xml:id="echoid-s207" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s208" xml:space="preserve">Hoc autem à nobis in hunc modum probabitur. <lb/></s> <s xml:id="echoid-s209" xml:space="preserve">Apparet lineam rectam <emph style="sc">AD</emph> in lineam rectam <emph style="sc">CE</emph> ca- <pb o="6" file="0006" n="14" rhead=""/> dere, ſicq́; </s> <s xml:id="echoid-s210" xml:space="preserve">binos angulos formare, angulũ ſcilicet <emph style="sc">CDA</emph>, <lb/> <anchor type="figure" xlink:label="fig-0006-01a" xlink:href="fig-0006-01"/> & </s> <s xml:id="echoid-s211" xml:space="preserve">angulum <emph style="sc">ADE</emph>: </s> <s xml:id="echoid-s212" xml:space="preserve">qui quidem bini anguli duobus re-<lb/>ctis ſunt æquales, ex decimatertia primi Euclidis pro-<lb/>poſitione. </s> <s xml:id="echoid-s213" xml:space="preserve">Quilibet autem trianguli æquilateri angu-<lb/>lus æqualis eſt duabus anguli recti tertiis, quod appa-<lb/>ret ex eo, quòd cujuſlibet trianguli tres anguli duobus <lb/>rectis ſunt æquales, ex trigeſima ſecunda primi Eucli-<lb/>dis. </s> <s xml:id="echoid-s214" xml:space="preserve">Præterea, ex eadem propoſitione, duo anguli <emph style="sc">DEA</emph> <lb/>& </s> <s xml:id="echoid-s215" xml:space="preserve"><emph style="sc">EAD</emph> æquales ſunt duabus tertiis anguli recti: </s> <s xml:id="echoid-s216" xml:space="preserve">&</s> <s xml:id="echoid-s217" xml:space="preserve">, per <lb/>primam partem quintæ propoſitionis primi Euclidis, <lb/>duo anguli <emph style="sc">DEA</emph> & </s> <s xml:id="echoid-s218" xml:space="preserve"><emph style="sc">EAD</emph> ſunt æquales: </s> <s xml:id="echoid-s219" xml:space="preserve">vnuſquiſq; </s> <s xml:id="echoid-s220" xml:space="preserve">er-<lb/>go eorum æqualis tertiæ parti anguli recti: </s> <s xml:id="echoid-s221" xml:space="preserve">ſicq́ angu-<lb/>lus <emph style="sc">EAC</emph> tribus tertiis anguli recti æquipollebit. </s> <s xml:id="echoid-s222" xml:space="preserve">Ergo <lb/>angulus rectus: </s> <s xml:id="echoid-s223" xml:space="preserve">quod demonſtrandum ſuſceperamus.</s> <s xml:id="echoid-s224" xml:space="preserve"/> </p> <div xml:id="echoid-div7" type="float" level="2" n="1"> <figure xlink:label="fig-0006-01" xlink:href="fig-0006-01a"> <image file="0006-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0006-01"/> </figure> </div> </div> <div xml:id="echoid-div9" type="section" level="1" n="7"> <head xml:id="echoid-head11" xml:space="preserve">OPERATIO III.</head> <p> <s xml:id="echoid-s225" xml:space="preserve"><emph style="sc">Data</emph> linea recta non terminata, & </s> <s xml:id="echoid-s226" xml:space="preserve">extra <lb/>eam puncto dato, ab eo puncto perpendicu-<lb/>larem ducere in dictam lineam.</s> <s xml:id="echoid-s227" xml:space="preserve"/> </p> <pb o="7" file="0007" n="15" rhead=""/> <p> <s xml:id="echoid-s228" xml:space="preserve">Sit linea non terminata <emph style="sc">AB</emph>: </s> <s xml:id="echoid-s229" xml:space="preserve">punctum verò extra <lb/>eam datum <emph style="sc">C</emph>, à quo volumus in dictam lineam per-<lb/>pendicularem lineam ducere. </s> <s xml:id="echoid-s230" xml:space="preserve">Primò pedem circini im <lb/>mobilem figemus in dicto puncto <emph style="sc">C</emph>: </s> <s xml:id="echoid-s231" xml:space="preserve">alterum pedem <lb/>extendemus donec datam lineam interſecet: </s> <s xml:id="echoid-s232" xml:space="preserve">quod ſi <lb/>primò nequeat, extendemus donec fieri poſſit interſe-<lb/>ctio: </s> <s xml:id="echoid-s233" xml:space="preserve">& </s> <s xml:id="echoid-s234" xml:space="preserve">cum hac apertura circulum deſcribemus, qui <lb/>quidem circulus lineam in duobus punctis interſeca-<lb/>bit, ſcilicet in <emph style="sc">D</emph> & </s> <s xml:id="echoid-s235" xml:space="preserve"><emph style="sc">E</emph>: </s> <s xml:id="echoid-s236" xml:space="preserve">à puncto verò <emph style="sc">C</emph> ad duo puncta <lb/><emph style="sc">D</emph> & </s> <s xml:id="echoid-s237" xml:space="preserve"><emph style="sc">E</emph>, duas lineas rectas ducemus, quæ erũt <emph style="sc">DC</emph> & </s> <s xml:id="echoid-s238" xml:space="preserve"><emph style="sc">CE</emph>, <lb/>& </s> <s xml:id="echoid-s239" xml:space="preserve">angulum <emph style="sc">DCE</emph> diuidemus in duas partes æquales <lb/>per lineam <emph style="sc">CF</emph>: </s> <s xml:id="echoid-s240" xml:space="preserve">quæ quidem diuiſio hoc pacto fiet. </s> <s xml:id="echoid-s241" xml:space="preserve">Pe-<lb/>dem circini immobilem collocabimus in puncto <emph style="sc">C</emph>, & </s> <s xml:id="echoid-s242" xml:space="preserve"><lb/>cum mobili pede deſcribemus portionẽ circuli, quæ <lb/>ſecet in punctis <emph style="sc">G</emph> & </s> <s xml:id="echoid-s243" xml:space="preserve"><emph style="sc">H</emph>, duo latera <emph style="sc">DC</emph> & </s> <s xml:id="echoid-s244" xml:space="preserve"><emph style="sc">CE</emph>, quæ angu-<lb/>lum <emph style="sc">DCE</emph> continent: </s> <s xml:id="echoid-s245" xml:space="preserve">arcum autem <emph style="sc">GH</emph> diuidemus in <lb/>duas æquales partes in puncto <emph style="sc">I</emph>: </s> <s xml:id="echoid-s246" xml:space="preserve">& </s> <s xml:id="echoid-s247" xml:space="preserve">à puncto <emph style="sc">C</emph> ad pun <lb/>ctum <emph style="sc">I</emph> lineam rectam ducemus: </s> <s xml:id="echoid-s248" xml:space="preserve">ſicq́; </s> <s xml:id="echoid-s249" xml:space="preserve">linea <emph style="sc">CI</emph> diuidet <lb/>angulum <emph style="sc">DCE</emph>, in duas partes æquales, vt oſtendit no-<lb/>na propoſitio primi Euclidis: </s> <s xml:id="echoid-s250" xml:space="preserve">lineam autem <emph style="sc">CI</emph> pro-<lb/> <anchor type="figure" xlink:label="fig-0007-01a" xlink:href="fig-0007-01"/> <pb o="8" file="0008" n="16" rhead=""/> ducemus aduſq; </s> <s xml:id="echoid-s251" xml:space="preserve">punctum <emph style="sc">F</emph>: </s> <s xml:id="echoid-s252" xml:space="preserve">eritq́; </s> <s xml:id="echoid-s253" xml:space="preserve">linea <emph style="sc">CF</emph> perpendi-<lb/>cularis vt ſuprà, vt oſtendit duodecima propoſitio <lb/>primi Euclidis.</s> <s xml:id="echoid-s254" xml:space="preserve"/> </p> <div xml:id="echoid-div9" type="float" level="2" n="1"> <figure xlink:label="fig-0007-01" xlink:href="fig-0007-01a"> <image file="0007-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0007-01"/> </figure> </div> <p> <s xml:id="echoid-s255" xml:space="preserve">Verùm, ad praxim accedens, data linea <emph style="sc">AB</emph>, & </s> <s xml:id="echoid-s256" xml:space="preserve">pun-<lb/>cto <emph style="sc">C</emph> dato, ſtatuam pedem immobilem circini in pun-<lb/>cto <emph style="sc">C</emph>, & </s> <s xml:id="echoid-s257" xml:space="preserve">cum pede mobili partem circuli deſcribam, <lb/>quæ ſecet lineam <emph style="sc">AB</emph> in duobus punctis: </s> <s xml:id="echoid-s258" xml:space="preserve">quod ſi fieri <lb/>nequeat, producam dictam lineam vel ab vna parte <lb/>vel ab alia, quouſque ſecari poſſit à dicto circulo in <lb/>duobus punctis.</s> <s xml:id="echoid-s259" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s260" xml:space="preserve">Ac primò ſtatuamus dictam lineam à neutra parte <lb/>productam eſſe, nihilominus tamen ſectam eſſe à dicto <lb/>circulo in duobus punctis, ſcilicet in <emph style="sc">D</emph> & </s> <s xml:id="echoid-s261" xml:space="preserve"><emph style="sc">E</emph>, vt ex figu-<lb/>ra apparet.</s> <s xml:id="echoid-s262" xml:space="preserve"/> </p> <figure> <image file="0008-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0008-01"/> </figure> <p> <s xml:id="echoid-s263" xml:space="preserve">Secundò, ſtatuamus dictum circulum lineam <emph style="sc">AB</emph> <lb/>in duobus punctis non ſecare, ſed ſolùm in puncto <emph style="sc">D</emph>, <lb/>à parte <emph style="sc">B</emph>, vt in figura apparet.</s> <s xml:id="echoid-s264" xml:space="preserve"/> </p> <pb o="9" file="0009" n="17" rhead=""/> <figure> <image file="0009-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0009-01"/> </figure> <p> <s xml:id="echoid-s265" xml:space="preserve">Produces lineam à parte <emph style="sc">A</emph>, quouſque ſecari poſſit à <lb/>dicto circulo in pũcto <emph style="sc">E</emph>, vt apparet in ſequenti figura.</s> <s xml:id="echoid-s266" xml:space="preserve"/> </p> <figure> <image file="0009-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0009-02"/> </figure> <p> <s xml:id="echoid-s267" xml:space="preserve">Tertiò, ſi circulus tantummodo lineam ſecet in <lb/>puncto <emph style="sc">E</emph>, ex parte <emph style="sc">A</emph>, non autem ex parte <emph style="sc">B</emph>, vt apparet <lb/>in figura:</s> <s xml:id="echoid-s268" xml:space="preserve"/> </p> <pb o="10" file="0010" n="18" rhead=""/> <figure> <image file="0010-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0010-01"/> </figure> <p> <s xml:id="echoid-s269" xml:space="preserve">Tunc producenda erit linea à parte <emph style="sc">B</emph>, quouſque <lb/>eam circulus ſecare poſſit in puncto <emph style="sc">D</emph>, vt apparet in <lb/>figura.</s> <s xml:id="echoid-s270" xml:space="preserve"/> </p> <figure> <image file="0010-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0010-02"/> </figure> <p> <s xml:id="echoid-s271" xml:space="preserve">Quartò, ſi circulus lineam <emph style="sc">AB</emph> nullibi ſecet, quia <lb/>circulus is extra lineam eſt ex parte <emph style="sc">A</emph>, vt videre eſt in <lb/>figura:</s> <s xml:id="echoid-s272" xml:space="preserve"/> </p> <pb o="11" file="0011" n="19" rhead=""/> <figure> <image file="0011-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0011-01"/> </figure> <p> <s xml:id="echoid-s273" xml:space="preserve">Producetur dicta linea à parte <emph style="sc">A</emph>, quouſque ſecetur <lb/>in punctis <emph style="sc">D</emph> & </s> <s xml:id="echoid-s274" xml:space="preserve"><emph style="sc">E</emph>, vt apparet in figura.</s> <s xml:id="echoid-s275" xml:space="preserve"/> </p> <figure> <image file="0011-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0011-02"/> </figure> <p> <s xml:id="echoid-s276" xml:space="preserve">Quod autem factum eſt, vbi circulus lineam non <lb/>ſecat à parte <emph style="sc">A</emph>, itidem fieri deberet, ſi circulus lineam <lb/>non ſecaret à parte B.</s> <s xml:id="echoid-s277" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s278" xml:space="preserve">Indicatis iis quæ ſuprà, viam oſtendemus, qua per-<lb/>pendicularis ducatur à puncto dato ſupra lineam da-<lb/>tam, productam, ſeu non productam. </s> <s xml:id="echoid-s279" xml:space="preserve">Quod vt con-<lb/>ſequamur, ſtatuemus pedem circini immobilem in <lb/>punctis <emph style="sc">D</emph> & </s> <s xml:id="echoid-s280" xml:space="preserve"><emph style="sc">E</emph>, deſcribendo duas circuli portiunculas <lb/>ex oppoſito puncti dati, quæ ſeſe in vno puncto in-<lb/>terſecent, in puncto ſcilicet <emph style="sc">F</emph>, vt videre eſt in figura.</s> <s xml:id="echoid-s281" xml:space="preserve"/> </p> <pb o="12" file="0012" n="20" rhead=""/> <figure> <image file="0012-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0012-01"/> </figure> <p> <s xml:id="echoid-s282" xml:space="preserve">Quo facto, adhibita regula vel norma ad puncta <emph style="sc">C</emph> <lb/>& </s> <s xml:id="echoid-s283" xml:space="preserve"><emph style="sc">F</emph>, ducetur linea <emph style="sc">CG</emph> à puncto <emph style="sc">C</emph> in lineam <emph style="sc">AB</emph>, vt vi-<lb/>dere eſt in hac figura:</s> <s xml:id="echoid-s284" xml:space="preserve"/> </p> <figure> <image file="0012-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0012-02"/> </figure> <p> <s xml:id="echoid-s285" xml:space="preserve">Sicq́; </s> <s xml:id="echoid-s286" xml:space="preserve">linea <emph style="sc">CG</emph>, perpendicularis erit in lineam <emph style="sc">AB</emph>, <lb/>productam, vel non productam.</s> <s xml:id="echoid-s287" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div11" type="section" level="1" n="8"> <head xml:id="echoid-head12" xml:space="preserve">OPERATIO IIII.</head> <p> <s xml:id="echoid-s288" xml:space="preserve"><emph style="sc">Data</emph> linea recta, & </s> <s xml:id="echoid-s289" xml:space="preserve">extra eam puncto <pb o="13" file="0013" n="21" rhead=""/> dato, ab eo puncto producere lineam æ qui-<lb/>diſtantem ſeu parallelam lineæ datæ.</s> <s xml:id="echoid-s290" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s291" xml:space="preserve">Sit linea data <emph style="sc">AB</emph>, punctum verò datum extra eam <lb/>ſit <emph style="sc">C</emph>, à puncto <emph style="sc">C</emph> ducemus lineam rectam æquidiſtan-<lb/>tem lineæ <emph style="sc">AB</emph> hunc in modum: </s> <s xml:id="echoid-s292" xml:space="preserve">Ducemus a puncto <emph style="sc">C</emph> <lb/>lineam rectam in lineam <emph style="sc">AB</emph>, quæ erit linea <emph style="sc">CE</emph>: </s> <s xml:id="echoid-s293" xml:space="preserve">ſicq́; </s> <s xml:id="echoid-s294" xml:space="preserve">ha <lb/>bebimus angulum <emph style="sc">CEA</emph>. </s> <s xml:id="echoid-s295" xml:space="preserve">Præterea ſupra lineam <emph style="sc">AB</emph> de-<lb/>ſcribemus angulum angulo <emph style="sc">CEA</emph> æqualem, angulum <lb/>ſcilicet <emph style="sc">FGA</emph>, idq́; </s> <s xml:id="echoid-s296" xml:space="preserve">per primam operationem, ſumpto <lb/>pro libito in dicta linea <emph style="sc">AB</emph> puncto <emph style="sc">G</emph>: </s> <s xml:id="echoid-s297" xml:space="preserve">quo facto facie-<lb/>mus lineam <emph style="sc">GF</emph> æqualem lineæ <emph style="sc">EC</emph>, per tertiam propo-<lb/>ſitionem primi Euclidis: </s> <s xml:id="echoid-s298" xml:space="preserve">deinde à puncto <emph style="sc">C</emph> ad pun-<lb/>ctum <emph style="sc">F</emph> ducemus lineam rectam, quæ erit <emph style="sc">CF</emph>.</s> <s xml:id="echoid-s299" xml:space="preserve"/> </p> <figure> <image file="0013-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0013-01"/> </figure> <p> <s xml:id="echoid-s300" xml:space="preserve">Quòd ſi probare velimus lineam <emph style="sc">CF</emph> lineæ <emph style="sc">AB</emph> æqui <lb/>diſtantem eſſe, id hoc pacto fiet. </s> <s xml:id="echoid-s301" xml:space="preserve">Angulus <emph style="sc">CEA</emph>, & </s> <s xml:id="echoid-s302" xml:space="preserve">an-<lb/>gulus <emph style="sc">FGA</emph> æquales ſunt ex ipſa conſtructione: </s> <s xml:id="echoid-s303" xml:space="preserve">linea <lb/>igitur <emph style="sc">CE</emph> æquidiſtans eſt lineæ <emph style="sc">GF</emph>, per primam partem <lb/>vigeſimæ octauæ propoſitionis primi Euclidis. </s> <s xml:id="echoid-s304" xml:space="preserve">Præte-<lb/>rea linea <emph style="sc">GF</emph> facta eſt æqualis lineæ <emph style="sc">CE</emph> per conſtructio-<lb/>nem: </s> <s xml:id="echoid-s305" xml:space="preserve">ſicq́; </s> <s xml:id="echoid-s306" xml:space="preserve">per trigeſimam tertiam primi Euclidis, li-<lb/>nea <emph style="sc">CF</emph> æquidiſtans erit lineæ <emph style="sc">AB</emph>, quod erat proban-<lb/>dum.</s> <s xml:id="echoid-s307" xml:space="preserve"/> </p> <pb o="14" file="0014" n="22" rhead=""/> <p> <s xml:id="echoid-s308" xml:space="preserve">Alio item belliſſimo modo duci poteſt linea æqui-<lb/>diſtans lineæ datæ à puncto extra eam dato. </s> <s xml:id="echoid-s309" xml:space="preserve">Sit da-<lb/>ta linea recta <emph style="sc">AB</emph>, extraq́; </s> <s xml:id="echoid-s310" xml:space="preserve">eam punctum datum <emph style="sc">C</emph>: </s> <s xml:id="echoid-s311" xml:space="preserve">duce <lb/>re volens à puncto <emph style="sc">C</emph> lineam æquidiſtantem lineæ <emph style="sc">AB</emph>, <lb/>ſtatuam pedem circini immobilem in puncto <emph style="sc">C</emph>, pe-<lb/>dem verò mobilem extendam, donec attingat lineam <lb/><emph style="sc">AB</emph> in puncto <emph style="sc">E</emph>: </s> <s xml:id="echoid-s312" xml:space="preserve">ſiſtendo, eadem circini apertura, pe-<lb/>dem immobilem in dicto puncto <emph style="sc">C</emph>, particulam arcus <lb/><emph style="sc">D</emph> deſcribam. </s> <s xml:id="echoid-s313" xml:space="preserve">Deinceps ſtatuendo pedem immobilem <lb/>in puncto <emph style="sc">E</emph> lineæ <emph style="sc">AB</emph>, cum altero pede ſecabo lineam <lb/><emph style="sc">AB</emph> in puncto <emph style="sc">F</emph>, eadem circini apertura, quæ eſt à pun-<lb/>cto <emph style="sc">C</emph> ad dictum arcum <emph style="sc">D</emph>. </s> <s xml:id="echoid-s314" xml:space="preserve">Præterea, figendo pedem <lb/>immobilem in puncto <emph style="sc">F</emph>, cum pede mobili ſecabimus <lb/>arcum <emph style="sc">D</emph> in puncto <emph style="sc">G</emph>, eadem circini apertura qua ſe-<lb/>cta eſt linea <emph style="sc">AB</emph> in puncto <emph style="sc">E</emph>, ſtatuendo pedem immo-<lb/>bilem in puncto <emph style="sc">C</emph>: </s> <s xml:id="echoid-s315" xml:space="preserve">ac à puncto <emph style="sc">C</emph> ad punctum <emph style="sc">G</emph>, duce-<lb/>mus lineam rectam, quæ erit linea <emph style="sc">CG</emph>. </s> <s xml:id="echoid-s316" xml:space="preserve">Dico ergo li-<lb/>neam <emph style="sc">CG</emph> æquidiſtantem eſſe lineæ <emph style="sc">AB</emph>. </s> <s xml:id="echoid-s317" xml:space="preserve">Quod facillimè <lb/>probari poteſt per trigeſimam quartam primi Eucli-<lb/>dis: </s> <s xml:id="echoid-s318" xml:space="preserve">ſupplementum enim figuræ perficiendo, latera op-<lb/>poſita æqualia erunt: </s> <s xml:id="echoid-s319" xml:space="preserve">quòd ſi æqualia, etiam æquidi-<lb/>ſtantia, quod erat mihi propoſitum.</s> <s xml:id="echoid-s320" xml:space="preserve"/> </p> <figure> <image file="0014-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0014-01"/> </figure> </div> <div xml:id="echoid-div12" type="section" level="1" n="9"> <head xml:id="echoid-head13" xml:space="preserve">OPERATIO QVINTA.</head> <p> <s xml:id="echoid-s321" xml:space="preserve"><emph style="sc">Haec</emph>operatio facit ad cognoſcendum <lb/>figurasrectilineas, æqualibus velinæqualibus <pb o="15" file="0015" n="23" rhead=""/> lateribus ſeu angulis præditas: </s> <s xml:id="echoid-s322" xml:space="preserve">item ad digno-<lb/>ſcendum an angulus figuræ æquilateræ & </s> <s xml:id="echoid-s323" xml:space="preserve">æ-<lb/>quiangulæ, major vel minor ſit recto. </s> <s xml:id="echoid-s324" xml:space="preserve">Ac pri-<lb/>mò de angulis figurarum rectilinearum a-<lb/>getur, vt innoteſcat quot angulis rectis illi æ-<lb/>quipolleant.</s> <s xml:id="echoid-s325" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s326" xml:space="preserve">Statuamus primò, figuram illam eſſe trium laterum: <lb/></s> <s xml:id="echoid-s327" xml:space="preserve">duo ſubtrahemus, remanebit vnum, quod duplicatum <lb/>duo facit: </s> <s xml:id="echoid-s328" xml:space="preserve">Triangulum igitur, ſeu trilatera figura, duos <lb/>angulos rectos habet. </s> <s xml:id="echoid-s329" xml:space="preserve">Secundò agamus de figura qua-<lb/>drilatera ſeu quatuor laterum: </s> <s xml:id="echoid-s330" xml:space="preserve">duobus ſubſtractis, duo <lb/>relinquentur, quibus duplicatis, fient quatuor. </s> <s xml:id="echoid-s331" xml:space="preserve">Qua-<lb/>dranguli ergo quatuor anguli, quatuor rectis ſunt æ-<lb/>quales. </s> <s xml:id="echoid-s332" xml:space="preserve">Tertiò ſuccedit Pentagonum, ſeu quinquelate-<lb/>ra figura: </s> <s xml:id="echoid-s333" xml:space="preserve">ex ea duobus lateribus ſubſtractis remane-<lb/>bunt tria, quibus duplicatis apparebit Pentagoni an-<lb/>gulos ſex rectis æquales eſſe. </s> <s xml:id="echoid-s334" xml:space="preserve">Ac per hanc regulam no-<lb/>bis innoteſcet quot rectis angulis æquipolleant angu-<lb/>li cujuſlibet figuræ rectilineæ. </s> <s xml:id="echoid-s335" xml:space="preserve">Iam ſi cupio dignoſcere <lb/>quantitatem anguli figuræ æquilateræ & </s> <s xml:id="echoid-s336" xml:space="preserve">æquiangulæ, <lb/>diuidam numerum angulorum rectorum quos ea fi-<lb/>gura complectitur, per numerum laterum ipſius figu-<lb/>ræ. </s> <s xml:id="echoid-s337" xml:space="preserve">Exempli gratia, Triangulum ſeu Trianguli anguli <lb/>duobus rectis ſunt æquales, quos partiemur cũ tribus <lb/>angulis ſeu lateribus figuræ, prodibunt duæ tertiæ an-<lb/>guli recti: </s> <s xml:id="echoid-s338" xml:space="preserve">angulus igitur cujuſlibet Trianguli æquilate-<lb/>ri duabus tertiis anguli recti æquipollet. </s> <s xml:id="echoid-s339" xml:space="preserve">Secundò, <lb/>quadrilatera figura quatuor angulis rectis æquipollet:</s> <s xml:id="echoid-s340" xml:space="preserve"> <pb o="16" file="0016" n="24" rhead=""/> Partiemur ergo quatuor angulos rectos, per quatuor <lb/>angulos quos figura complectitur. </s> <s xml:id="echoid-s341" xml:space="preserve">Quilibet igitur an-<lb/>gulus quadrati angulo recto æqualis eſt. </s> <s xml:id="echoid-s342" xml:space="preserve">Tertiò, Penta <lb/>gonum æquale eſt ſex angulis rectis, partiemur hoſce <lb/>ſex angulos per quinque angulos quos figura comple-<lb/>ctitur, prodibit angulus rectus, cũ quinta parte alterius. <lb/></s> <s xml:id="echoid-s343" xml:space="preserve">Ac cum hoc canone innoteſcet nobis vnuſquiſque an <lb/>gulus figuræ æquilateræ & </s> <s xml:id="echoid-s344" xml:space="preserve">æquiangulæ, quanto major <lb/>vel minor ſit angulo recto. </s> <s xml:id="echoid-s345" xml:space="preserve">Verùm hunc canonem me-<lb/>liùs & </s> <s xml:id="echoid-s346" xml:space="preserve">Geometricè explicemus. </s> <s xml:id="echoid-s347" xml:space="preserve">Primò ad indagandum <lb/>Trianguli æquilateri angulum an major vel minor ſit <lb/>recto, deſcribatur angulus rectus, vt factum eſt in pri-<lb/>ma figura ſequenti. </s> <s xml:id="echoid-s348" xml:space="preserve">Præterea diuidatur angulus hic re-<lb/>ctus in tres partes æquales, deſcribendo portionem <lb/>circuli, vt apparet in ſecunda figura. </s> <s xml:id="echoid-s349" xml:space="preserve">Ex his tribus par-<lb/>tibus duas ſumo, ad quarum extremitatem ab angulo <lb/>recto duco lineam, vt videre eſt in figura. </s> <s xml:id="echoid-s350" xml:space="preserve">Atque hoc <lb/>modo habeo angulum Trianguli æquilateri. </s> <s xml:id="echoid-s351" xml:space="preserve">Angulus <lb/>quadrati æqualis eſt angulo recto. </s> <s xml:id="echoid-s352" xml:space="preserve">Aſt, ad formandum <lb/>Pentagoni angulum, diuidemus angulum rectum in <lb/>quinque partes æquales, vt apparet in tertia figura. </s> <s xml:id="echoid-s353" xml:space="preserve">At <lb/>quoniam angulus pentagoni æqualis eſt angulo vni <lb/>recto, cum alterius quinta parte, ſumemus vnam ex il-<lb/>lis partibus, qua adjuncta angulo recto, ducemus li-<lb/>neam ab angulo recto ad finem illius additamenti, ha-<lb/>bebimusq́; </s> <s xml:id="echoid-s354" xml:space="preserve">effictum angulum Pentagoni æqui-<lb/>lateri, vt apparet infrà. </s> <s xml:id="echoid-s355" xml:space="preserve">Ac ſecundùm hunc <lb/>canonem fieri poterit omnis ope-<lb/>ratio, vt videre eſt in ſe-<lb/>quentibus fi-<lb/>guris.</s> <s xml:id="echoid-s356" xml:space="preserve"/> </p> <pb o="17" file="0017" n="25" rhead=""/> </div> <div xml:id="echoid-div13" type="section" level="1" n="10"> <head xml:id="echoid-head14" xml:space="preserve">_Prima figura._</head> <p> <s xml:id="echoid-s357" xml:space="preserve">Angulus rectus <lb/><emph style="sc">ABC</emph>.</s> <s xml:id="echoid-s358" xml:space="preserve"/> </p> <figure> <image file="0017-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0017-01"/> </figure> </div> <div xml:id="echoid-div14" type="section" level="1" n="11"> <head xml:id="echoid-head15" xml:space="preserve">_Secunda figura._</head> <p> <s xml:id="echoid-s359" xml:space="preserve">Angulus trianguli æqui-<lb/>lateri <emph style="sc">ABD</emph>.</s> <s xml:id="echoid-s360" xml:space="preserve"/> </p> <figure> <image file="0017-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0017-02"/> </figure> </div> <div xml:id="echoid-div15" type="section" level="1" n="12"> <head xml:id="echoid-head16" xml:space="preserve">_Tertia figura._</head> <p> <s xml:id="echoid-s361" xml:space="preserve">Angulus pentago-<lb/>ni æquilateri <lb/><emph style="sc">ABD</emph>.</s> <s xml:id="echoid-s362" xml:space="preserve"/> </p> <figure> <image file="0017-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0017-03"/> </figure> </div> <div xml:id="echoid-div16" type="section" level="1" n="13"> <head xml:id="echoid-head17" xml:space="preserve">_Quarta figura._</head> <p> <s xml:id="echoid-s363" xml:space="preserve">Angulus hexagoni <lb/>æquilateri <lb/><emph style="sc">ABD</emph>.</s> <s xml:id="echoid-s364" xml:space="preserve"/> </p> <figure> <image file="0017-04" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0017-04"/> </figure> </div> <div xml:id="echoid-div17" type="section" level="1" n="14"> <head xml:id="echoid-head18" xml:space="preserve">_Quinta figura._</head> <p> <s xml:id="echoid-s365" xml:space="preserve">Angulus ſeptanguli <lb/>æquilateri <emph style="sc">ABD</emph>.</s> <s xml:id="echoid-s366" xml:space="preserve"/> </p> <figure> <image file="0017-05" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0017-05"/> </figure> </div> <div xml:id="echoid-div18" type="section" level="1" n="15"> <head xml:id="echoid-head19" xml:space="preserve">_Sexta figura._</head> <p> <s xml:id="echoid-s367" xml:space="preserve">Angulus æquilateri <lb/>octanguli <emph style="sc">ABD</emph>.</s> <s xml:id="echoid-s368" xml:space="preserve"/> </p> <figure> <image file="0017-06" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0017-06"/> </figure> <pb o="18" file="0018" n="26" rhead=""/> </div> <div xml:id="echoid-div19" type="section" level="1" n="16"> <head xml:id="echoid-head20" xml:space="preserve">_Septima figura._</head> <p> <s xml:id="echoid-s369" xml:space="preserve">Angulus nonangu-<lb/>li æquilateri <lb/><emph style="sc">ABD</emph>.</s> <s xml:id="echoid-s370" xml:space="preserve"/> </p> <figure> <image file="0018-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0018-01"/> </figure> </div> <div xml:id="echoid-div20" type="section" level="1" n="17"> <head xml:id="echoid-head21" xml:space="preserve">_Octaua figura._</head> <p> <s xml:id="echoid-s371" xml:space="preserve">Angulus decago-<lb/>ni æquilateri <lb/><emph style="sc">ABD</emph>.</s> <s xml:id="echoid-s372" xml:space="preserve"/> </p> <figure> <image file="0018-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0018-02"/> </figure> </div> <div xml:id="echoid-div21" type="section" level="1" n="18"> <head xml:id="echoid-head22" xml:space="preserve">_Nona figura._</head> <p> <s xml:id="echoid-s373" xml:space="preserve">Angulus æquilateri <lb/>hendecagoni <lb/><emph style="sc">ABD</emph>.</s> <s xml:id="echoid-s374" xml:space="preserve"/> </p> <figure> <image file="0018-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0018-03"/> </figure> <pb o="19" file="0019" n="27" rhead=""/> </div> <div xml:id="echoid-div22" type="section" level="1" n="19"> <head xml:id="echoid-head23" xml:space="preserve">_Decima figura._</head> <p> <s xml:id="echoid-s375" xml:space="preserve">Angulus dodecagoni æquilateri <emph style="sc">ABD</emph>.</s> <s xml:id="echoid-s376" xml:space="preserve"/> </p> <figure> <image file="0019-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0019-01"/> </figure> </div> <div xml:id="echoid-div23" type="section" level="1" n="20"> <head xml:id="echoid-head24" xml:space="preserve">OPERATIO SEXTA.</head> <p> <s xml:id="echoid-s377" xml:space="preserve"><emph style="sc">Praeterea</emph>, vbi deſcribenda eſſet ichno-<lb/>graphia arcis vel propugnaculi, in eadem qui-<lb/>dem proportione quàm alia, verùm illâ major <lb/>vel minor. </s> <s xml:id="echoid-s378" xml:space="preserve">Verbigratia, ſi vellemus deſcribe-<lb/>reichnographiam arcis quarta parte majoris <lb/>alia, veluti ſi prima quatuor paſſuum eſſet, al-<lb/>tera verò deberet eſſe quinque, vt ſunt duæ li-<lb/>neæ <emph style="sc">AB, A, -- B,</emph> & </s> <s xml:id="echoid-s379" xml:space="preserve"><emph style="sc">CD, C -- D,</emph> <lb/>& </s> <s xml:id="echoid-s380" xml:space="preserve">linea <emph style="sc">AB</emph> prior ſit paſſuum 4, linea verò <emph style="sc">CD</emph> <lb/>paſſuum 5, tertia linea erit ea, in qua facta eſt <lb/>ſcala primæ ichnographiæ, quæ fieri debebit <lb/>major vel minor. </s> <s xml:id="echoid-s381" xml:space="preserve">Statuamus autem eam eſſe <pb o="20" file="0020" n="28" rhead=""/> lineam <emph style="sc">EF</emph>, paſſus 25 longam:</s> <s xml:id="echoid-s382" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s383" xml:space="preserve">E -- F.</s> <s xml:id="echoid-s384" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s385" xml:space="preserve">Ad hoc agendum formabimus angulum fortuitum <lb/><emph style="sc">GHI</emph>, & </s> <s xml:id="echoid-s386" xml:space="preserve">à linea <emph style="sc">HI</emph>, ſecabimus duas lineas. </s> <s xml:id="echoid-s387" xml:space="preserve">Prior erit <emph style="sc">HK</emph> <lb/>æqualis <emph style="sc">AB</emph>: </s> <s xml:id="echoid-s388" xml:space="preserve">altera <emph style="sc">KL</emph> æqualis <emph style="sc">CD</emph>. </s> <s xml:id="echoid-s389" xml:space="preserve">Et à linea <emph style="sc">HG</emph> ſecabi-<lb/>mus aliam æqualem <emph style="sc">EF</emph>, quæ erit <emph style="sc">HM</emph>: </s> <s xml:id="echoid-s390" xml:space="preserve">intra duo item <lb/>puncta <emph style="sc">K</emph> & </s> <s xml:id="echoid-s391" xml:space="preserve"><emph style="sc">M</emph>, ducemus lineam rectam, quæ erit <emph style="sc">KM</emph>: </s> <s xml:id="echoid-s392" xml:space="preserve">ac <lb/>à puncto <emph style="sc">L</emph> ducemus lineam æquidiſtantem lineæ <emph style="sc">KM</emph>, <lb/>vt docet quarta operatio, quæ erit linea <emph style="sc">LN</emph>: </s> <s xml:id="echoid-s393" xml:space="preserve">linea au-<lb/>tem <emph style="sc">MN</emph> erit quarta proportionalis ad tres lineas <emph style="sc">AB</emph>, <lb/><emph style="sc">CD</emph>, & </s> <s xml:id="echoid-s394" xml:space="preserve"><emph style="sc">EF</emph>, vt docet duodecima ſexti Euclidis Itaque li-<lb/>nea <emph style="sc">EF</emph>, quum ſit æqualis lineæ <emph style="sc">HM</emph>, eandem habebit <lb/>proportionem ad lineam <emph style="sc">MN</emph>, quam habet linea <emph style="sc">AB</emph>, <lb/>æqualis exiſtens lineæ <emph style="sc">HK</emph>, ad <emph style="sc">KL</emph>, quæ æqualis eſt <emph style="sc">CD</emph>. <lb/></s> <s xml:id="echoid-s395" xml:space="preserve">Iam ſumemus mediam proportionalem inter lineam <lb/><emph style="sc">HM</emph> & </s> <s xml:id="echoid-s396" xml:space="preserve"><emph style="sc">MN</emph>, per nonam ſexti Euclidis, quæ erit linea <lb/><emph style="sc">OP</emph>, <emph style="sc">O -- P</emph> <lb/>partiemurq́; </s> <s xml:id="echoid-s397" xml:space="preserve">lineam <emph style="sc">OP</emph>, in paſſus 25, prout erat diuiſa <lb/>linea <emph style="sc">EF</emph>, deſcribendoq́; </s> <s xml:id="echoid-s398" xml:space="preserve">ichnographiam ſimilem datæ, <lb/>cum ſcala <emph style="sc">OP</emph>, ichnographia quarta parte major erit <lb/>quàm prior, vt docet decima nona ſexti Euclidis. </s> <s xml:id="echoid-s399" xml:space="preserve">Ex <lb/>hoc eodem canone deſcribi poterit ichnographia <lb/>major vel minor, in quacumq; </s> <s xml:id="echoid-s400" xml:space="preserve">proportione libuerit. </s> <s xml:id="echoid-s401" xml:space="preserve"><lb/>Ne quis autem conqueratur quòd paſſus linearũ <emph style="sc">HM</emph>, <lb/>& </s> <s xml:id="echoid-s402" xml:space="preserve"><emph style="sc">MN</emph> inæquales ſint paſſibus linearum <emph style="sc">HK</emph>, & </s> <s xml:id="echoid-s403" xml:space="preserve"><emph style="sc">KL</emph>: </s> <s xml:id="echoid-s404" xml:space="preserve">ſi <lb/>enim vtrobique æqualitas à nobis obſeruata ſuiſſet, <lb/>aut in nimiam longitudinem excreuiſſet typus ſeu fi-<lb/>gura, aut æquidiſtantia linearum <emph style="sc">KM</emph> & </s> <s xml:id="echoid-s405" xml:space="preserve"><emph style="sc">LN</emph> diſcerni <lb/>nequiuiſſet.</s> <s xml:id="echoid-s406" xml:space="preserve"/> </p> <pb o="21" file="0021" n="29" rhead=""/> <figure> <image file="0021-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0021-01"/> </figure> <pb o="22" file="0022" n="30" rhead=""/> </div> <div xml:id="echoid-div24" type="section" level="1" n="21"> <head xml:id="echoid-head25" xml:space="preserve">SEPTIMA OPERATIO.</head> <p> <s xml:id="echoid-s407" xml:space="preserve"><emph style="sc">Indagare</emph> mediam proportionalem in-<lb/>ter duas lineas.</s> <s xml:id="echoid-s408" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s409" xml:space="preserve">Verbi gratia, deſidero mediam proportionalem in-<lb/>ter lineam E -- F, & </s> <s xml:id="echoid-s410" xml:space="preserve">F -- G, jun-<lb/>gam eas in directum, faciamq́; </s> <s xml:id="echoid-s411" xml:space="preserve">ex eis vnicam lineam, <lb/>quæ erit <emph style="sc">E -- F -- G</emph>, æ quipollens <lb/>ſcilicet E F & </s> <s xml:id="echoid-s412" xml:space="preserve">F G.</s> <s xml:id="echoid-s413" xml:space="preserve"> Diuidemus deinde integram lineam <lb/><emph style="sc">EG</emph> in duas partes æ quales in puncto <emph style="sc">O</emph>, vt hîc apparet, <lb/><emph style="sc">E -- F -- O -- G</emph>, figemusq́; </s> <s xml:id="echoid-s414" xml:space="preserve">pedem im-<lb/>mobilem circini in puncto <emph style="sc">O</emph>, alterum extendendo ad <lb/>alterutram extremitatum <emph style="sc">E</emph> vel <emph style="sc">G</emph>, ſemicirculumq́; </s> <s xml:id="echoid-s415" xml:space="preserve">de-<lb/>ſcribemus: </s> <s xml:id="echoid-s416" xml:space="preserve">deinde à puncto <emph style="sc">F</emph> erigemus perpendicu-<lb/>larem, vt in ſecunda operatione factum eſt, quæ erit <lb/>linea <emph style="sc">FH</emph>, quam dico mediam eſſe proportionalem in-<lb/>ter duas lineas EF, & </s> <s xml:id="echoid-s417" xml:space="preserve">FG, vt docet nona ſexti Eucli-<lb/>dis.</s> <s xml:id="echoid-s418" xml:space="preserve"/> </p> <figure> <image file="0022-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0022-01"/> </figure> <pb o="23" file="0023" n="31" rhead=""/> </div> <div xml:id="echoid-div25" type="section" level="1" n="22"> <head xml:id="echoid-head26" xml:space="preserve">OPERATIO OCTAVA.</head> <p> <s xml:id="echoid-s419" xml:space="preserve"><emph style="sc">Lineam</emph> rectam in aliquot partes æquales <lb/>diuidere.</s> <s xml:id="echoid-s420" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s421" xml:space="preserve">Primò formabimus duos angulos æ quales, vnum in <lb/>vna extremitate dictæ lineæ, alterum verò in altera: </s> <s xml:id="echoid-s422" xml:space="preserve">idq́; <lb/></s> <s xml:id="echoid-s423" xml:space="preserve">per primam operationem. </s> <s xml:id="echoid-s424" xml:space="preserve">Deinde diuidemus vnum-<lb/>quodque latus (quorum ope angulos formauimus) <lb/>in tot partes in quot volumus diuidere lineam datam, <lb/>vnica excepta: </s> <s xml:id="echoid-s425" xml:space="preserve">& </s> <s xml:id="echoid-s426" xml:space="preserve">adhibita regula ducemus lineas, quæ <lb/>interſecent lineam datam, ſicq́; </s> <s xml:id="echoid-s427" xml:space="preserve">linea data apparebit <lb/>diuiſa in tot partes in quot erat à nobis diuidenda.</s> <s xml:id="echoid-s428" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s429" xml:space="preserve">Exempli gratia, ſtatuamus lineam <emph style="sc">AB</emph>, diuidendam <lb/><emph style="sc">A -- B</emph>, <lb/>eſſe in partes octo: </s> <s xml:id="echoid-s430" xml:space="preserve">formabimus duos angulos, vnum <lb/>in puncto <emph style="sc">A</emph>, qui erit angulus <emph style="sc">DAB</emph>, alterum verò in <lb/>puncto <emph style="sc">B</emph>, qui erit angulus <emph style="sc">CBA</emph>, vt in figura apparet.</s> <s xml:id="echoid-s431" xml:space="preserve"/> </p> <figure> <image file="0023-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0023-01"/> </figure> <pb o="24" file="0024" n="32" rhead=""/> <p> <s xml:id="echoid-s432" xml:space="preserve">Præterea diuidemus lineas BC, & </s> <s xml:id="echoid-s433" xml:space="preserve">AD, vtramque in <lb/>ſeptem partes æ quales, vt ex hac figura liquet.</s> <s xml:id="echoid-s434" xml:space="preserve"/> </p> <figure> <image file="0024-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0024-01"/> </figure> <p> <s xml:id="echoid-s435" xml:space="preserve">Hoc facto adhibebimus regulam ad puncta vtriuſ-<lb/>que ſibi inuicem oppoſita, ſicq́; </s> <s xml:id="echoid-s436" xml:space="preserve">ſecabitur linea <emph style="sc">AB</emph> in <lb/>octo partes, vt indicat ſequens figura.</s> <s xml:id="echoid-s437" xml:space="preserve"/> </p> <figure> <image file="0024-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0024-02"/> </figure> <pb o="25" file="0025" n="33" rhead=""/> <p> <s xml:id="echoid-s438" xml:space="preserve">Per hanc methodum vnaquæque linea diuidi pote-<lb/>rit in quotcumque voluerimus ſectiones, vt videre eſt <lb/>in ſequenti figura.</s> <s xml:id="echoid-s439" xml:space="preserve"/> </p> <figure> <image file="0025-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0025-01"/> </figure> <figure> <image file="0025-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0025-02"/> </figure> <pb o="26" file="0026" n="34"/> <figure> <image file="0026-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0026-01"/> </figure> </div> <div xml:id="echoid-div26" type="section" level="1" n="23"> <head xml:id="echoid-head27" xml:space="preserve">Quomodo poſsint deſignari arces <lb/>ſeu propugnacula, cum eorum <lb/>menſuris, aliísque rebus, quæ ſibi <lb/>competunt.</head> <head xml:id="echoid-head28" xml:space="preserve">CAPVT SECVNDVM.</head> <p> <s xml:id="echoid-s440" xml:space="preserve"><emph style="sc">PRimo</emph> capite explicauimus pleraſque o-<lb/>perationes geometricas, quas diximus <lb/>neceſſarias eſſe ad deſignãdas arces, pro-<lb/>pugnacula, vel caſtra, necnon & </s> <s xml:id="echoid-s441" xml:space="preserve">muros <lb/>rectos (quos Galli courtince dicunt, quós-<lb/>que poſthac cortinas nuncupabimus,) ab vno propu-<lb/>gnaculo ad aliud: </s> <s xml:id="echoid-s442" xml:space="preserve">at que etiam ad caſtrametandum, a-<lb/>liaq́; </s> <s xml:id="echoid-s443" xml:space="preserve">ejus generis perficienda. </s> <s xml:id="echoid-s444" xml:space="preserve">Hæc enim omnia vix, ac <lb/>ne vix quidem, certò deſcribi poſſent abſque opera-<lb/>tionibus præfatis. </s> <s xml:id="echoid-s445" xml:space="preserve">Initio igitur ſumpto à dictis opera-<lb/>tionibus, easq́; </s> <s xml:id="echoid-s446" xml:space="preserve">ad noſtrum inſtitutum aptando, in hoc <lb/>capite præſcribetur canon ad ipſa propugnacula deſi-<lb/>gnanda, vnà cum ſuis menſuris, aliisq́; </s> <s xml:id="echoid-s447" xml:space="preserve">rebus ejuſdem <lb/>argumenti, idq́; </s> <s xml:id="echoid-s448" xml:space="preserve">quàm fieri poterit breuiſſimè, ac facil-<lb/>limè. </s> <s xml:id="echoid-s449" xml:space="preserve">Hic autem canon inſeruiet ad conſtructionem <lb/>integrorum propugnaculorum, ſemipropugnaculo-<lb/>rum, minorum integro, minorum dimidiato: </s> <s xml:id="echoid-s450" xml:space="preserve">fientq́; <lb/></s> <s xml:id="echoid-s451" xml:space="preserve">ea propugnacula ita capacia, vt opportunè poſſint à <lb/>latere tueri arces vel caſtra in quibus ea fabricare con-<lb/>ſtituimus, (Galli dicũt flanqucr) ſiue ſint in monte, ſiue <pb o="27" file="0027" n="35" rhead=""/> in planitie. </s> <s xml:id="echoid-s452" xml:space="preserve">Ac primò, antequam ad fabricam venia-<lb/>mus, attentè conſiderandum eſt, qua ex parte hoſtis <lb/>majus inferre poſſit damnum, ac quomodo fieri poſ-<lb/>ſit, vt propugnaculum meliùs tueatur arcem ſeu ca-<lb/>ſtrum. </s> <s xml:id="echoid-s453" xml:space="preserve">Perpendendum eſt etiam, an velimus for-<lb/>mare propugnaculum cum cuniculo tranſuerſo (Gal-<lb/>li dicunt contzcminc,) vel puteis (fiunt autem hi in imo <lb/>propugnaculi vel cortinæ, ad aperiendos & </s> <s xml:id="echoid-s454" xml:space="preserve">vanos <lb/>reddendos cuniculos vel furnos, qui ab hoſtibus <lb/>fiunt.) </s> <s xml:id="echoid-s455" xml:space="preserve">Hi autem cuniculi tranſuerſi vel putei antiqui-<lb/>tus non fiebant, niſi vbi arces aqua non circumda-<lb/>bantur: </s> <s xml:id="echoid-s456" xml:space="preserve">hodie verò fiunt & </s> <s xml:id="echoid-s457" xml:space="preserve">cum aqua & </s> <s xml:id="echoid-s458" xml:space="preserve">abſque aqua, <lb/>propter furnos qui fiunt in cortina & </s> <s xml:id="echoid-s459" xml:space="preserve">circa propu-<lb/>gnacula ſuper aquam. </s> <s xml:id="echoid-s460" xml:space="preserve">Certum autem eſt, dari non poſ-<lb/>ſe canonem generalem ſuper menſuris, quia conſtruun <lb/>tur majora vel minora ſecundùm ſitum, ac juxta ſum-<lb/>ptus quos in eis vel poſſumus vel volumus facere. </s> <s xml:id="echoid-s461" xml:space="preserve">Con <lb/>uenit autem ei qui animum appellit ad hanc ſcien-<lb/>tiam deſignandi rite propugnacula ſeu arces, conue-<lb/>nit, inquam, ei, vt ſecundùm canones in hoc opere ex-<lb/>plicatos, ſciat in charta deſcribere quoduis genus pro-<lb/>pugnaculi, vel etiam modulos eorum erigere (Galli <lb/>vocant modcſſc@) in iisq́; </s> <s xml:id="echoid-s462" xml:space="preserve">exactè menſuras obſeruare, vt <lb/>cõmunicando cũ variis hominibusſuas delineationes, <lb/>audire poſſit varia eorũ judicia. </s> <s xml:id="echoid-s463" xml:space="preserve">Videat etiam quid pro <lb/>priè competat arcibus quæ in montibus extruuntur, <lb/>iis quæ in planitiebus, iis quæ alibi, Iam ſtatuamus de-<lb/>ſignandum nobis eſſe propugnaculum cum cunicu-<lb/>lo tranſuerſo, ea tamen lege vt eo poſſimus vti abſque <lb/>eo cuniculo. </s> <s xml:id="echoid-s464" xml:space="preserve">Erigatur autem hoc noſtrum propugna-<lb/>culum ſuper figura pentagona æ quilatera & </s> <s xml:id="echoid-s465" xml:space="preserve">æquian- <pb o="28" file="0028" n="36" rhead=""/> gula, vt videre eſt in figura ſequenti <emph style="sc">ABCDE</emph>.</s> <s xml:id="echoid-s466" xml:space="preserve"/> </p> <figure> <image file="0028-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0028-01"/> </figure> <p> <s xml:id="echoid-s467" xml:space="preserve">Velimus autem id formare ſuper angulo <emph style="sc">ABC</emph> dua-<lb/>rum arearum, ſeu platear m (Galli vocant place,) al-<lb/>terum ad cingulũ vſq; </s> <s xml:id="echoid-s468" xml:space="preserve">pedes 27 (Galli vocant cordoy:) <lb/></s> <s xml:id="echoid-s469" xml:space="preserve">aſcendatq́; </s> <s xml:id="echoid-s470" xml:space="preserve">ita, vt in ſingulos quinos pedes altitudinis <lb/>pes vnus latitudinis depereat: </s> <s xml:id="echoid-s471" xml:space="preserve">(Galli vocant cy talut, cy <lb/>cſch 2pc, cy augiuc: </s> <s xml:id="echoid-s472" xml:space="preserve">inclinato opere, vel operis inclinatio <lb/>nem, poſthac dicemus.) </s> <s xml:id="echoid-s473" xml:space="preserve">ſufficit enim hæc muri inclina-<lb/>tio ſatis ſuperq́;</s> <s xml:id="echoid-s474" xml:space="preserve">. Quamuis certum ſit, quo magis incli-<lb/>nat muri fabrica, eo minus glandes ſeu pilas bombar-<lb/>darum hoſtilium eum offendere, quia obliquè, non re <lb/>ctà feriunt. </s> <s xml:id="echoid-s475" xml:space="preserve">Verùm hæc omnia cum judicio diſpenſa-<lb/>ri debent. </s> <s xml:id="echoid-s476" xml:space="preserve">Nam vbi hæc inclinatio longiùs à perpendi-<lb/>culo diſcederet, periculum eſſet ne ſuperior pars infe-<lb/>riorem adeò premeret, vt ob id murus aperiretur ac <lb/>peſſumdaretur, pedem amittendo. </s> <s xml:id="echoid-s477" xml:space="preserve">Animaduertendum <pb o="29" file="0029" n="37" rhead=""/> eſt etiam, quando arces ſeu propugnacula conſtruun-<lb/>tur in vicinia loci alicujus eminentis, ita vt locus il-<lb/>le ſuperemineat arci noſtræ (hanc ſupereminentiam <lb/>Galli dicunt eſtrc à cauaſſicr), tunc ita debet conſtrui <lb/>propugnaculum, vt rectà opponatur loco illi eminen-<lb/>ti, nec permittendum vt locus ille eminens ſit vnquam <lb/>è regione cortinæ arcis noſtræ, ne per cortinam arx <lb/>noſtra offendatur, ſic enim ea omni propugnatione, <lb/>ſeu defenſione, priuaretur. </s> <s xml:id="echoid-s478" xml:space="preserve">Antequam autem ad <lb/>propugnaculi fabricam accedamus, ſigillatim debent <lb/>ſuæ quælibet menſuræ ſupputari, tum longitudinis, <lb/>tum latitudinis, vt dignoſcatur capacitas ſoli quod de-<lb/>bet fundamentum propugnaculi occupare. </s> <s xml:id="echoid-s479" xml:space="preserve">Vt ergo <lb/>innoteſcant eæ menſuræ, conſtituamus dare huic pro-<lb/>pugnaculo quinque pedes cum dimidio inclinatio-<lb/>nis, in altitudine verò 27 ad cingulum vſque, in craſſi-<lb/>tie quatuor, idq́; </s> <s xml:id="echoid-s480" xml:space="preserve">circa cingulum: </s> <s xml:id="echoid-s481" xml:space="preserve">nam fundamento <lb/>pedem vnum ſolummodo deputo, quia paulatim ſpiſ-<lb/>ſitudo muri creſcit donec circa cingulum ad quatuor <lb/>pedes peruenerit. </s> <s xml:id="echoid-s482" xml:space="preserve">Pedes item quatuor do latitudini cu-<lb/>niculi tranſuerſi, & </s> <s xml:id="echoid-s483" xml:space="preserve">4 alios ſpiſſitudini muri pro cuni-<lb/>culo tranſuerſo: </s> <s xml:id="echoid-s484" xml:space="preserve">quindecim item calcaribus, ſiue con-<lb/>trafortiis, (Galli vocant eſpczons el contzcfozts, Vitruuius <lb/>videtur vocaſſe anteridas, & </s> <s xml:id="echoid-s485" xml:space="preserve">eriſmas) idq́, vltra murum <lb/>cuniculi tranſuerſi: </s> <s xml:id="echoid-s486" xml:space="preserve">& </s> <s xml:id="echoid-s487" xml:space="preserve">in ſummitate ejus muri calcaria <lb/>ea extendentur ad murum vſq; </s> <s xml:id="echoid-s488" xml:space="preserve">qui jungitur operi in-<lb/>clinato, (Galli, muzaiſſe dc ſ eſcharpc) donec ad cingu-<lb/>lum veniatur. </s> <s xml:id="echoid-s489" xml:space="preserve">Præterea ſtatuentur pedes 20 aperturæ <lb/>ſiue extenſionis pro area ſeu platea inferiori, idq́; </s> <s xml:id="echoid-s490" xml:space="preserve">pro <lb/>minima longitudine propugnaculi. </s> <s xml:id="echoid-s491" xml:space="preserve">Alij autumant ſa-<lb/>tius fore, ſi areæ ſeu plateæ ſint omnino apertæ, quia <pb o="30" file="0030" n="38" rhead=""/> hoc pacto fierent abſque columnis (Galli dicunt pila-<lb/>ſtzce:) </s> <s xml:id="echoid-s492" xml:space="preserve">columnæ autem illæ adhibentur, quando pars <lb/>areæ inferioris eſt cooperta, quod magis laudo: </s> <s xml:id="echoid-s493" xml:space="preserve">quia <lb/>imbrium tempore puluis bombardicus ſartus tectus <lb/>remanet, & </s> <s xml:id="echoid-s494" xml:space="preserve">milites poſſunt ſecuriùs arcem defendere, <lb/>minorq́; </s> <s xml:id="echoid-s495" xml:space="preserve">expenſa fit in extructione. </s> <s xml:id="echoid-s496" xml:space="preserve">13 autem pedes <lb/>dabimus latitudini loricæ ſeu corollæ, (Galli vocant <lb/>parapects) in qua fient feneſtræ tormentariæ plateæ ſu-<lb/>perioris: </s> <s xml:id="echoid-s497" xml:space="preserve">ſtatuimus autem hanc corollam fabricatam <lb/>eſſe ſuper pila muri ſolidi, initium ſumendo à funda-<lb/>mento, quod eſt pedum 15, vt apparebit in figuris ſe-<lb/>quentibus.</s> <s xml:id="echoid-s498" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s499" xml:space="preserve">Dabimus præterea pedes 60 pro retroceſſione pla-<lb/>teæ ſuperioris. </s> <s xml:id="echoid-s500" xml:space="preserve">Hæ ſupradictæ menſuræ, ſimul junctæ, <lb/>faciunt pedes 127 cum dimidio (quod dilucidiùs ap-<lb/>parebit in noſtris typis ſeu figuris, ex ſcalis ſuis, menſu-<lb/>ris videlicet diſtributis in paſſus & </s> <s xml:id="echoid-s501" xml:space="preserve">pedes Venetos, <lb/>quinque pedes vnicuique paſſui tribuendo.) </s> <s xml:id="echoid-s502" xml:space="preserve">Sunt au-<lb/>tem hi pedes 127 cum dimidio, paſſus 25, cum duobus <lb/>pedibus: </s> <s xml:id="echoid-s503" xml:space="preserve">hæcq́; </s> <s xml:id="echoid-s504" xml:space="preserve">erit longitudo, quæ eſt ab angulo la-<lb/>teris, ad angulum qui ambas cortinas conficit, quas <lb/>imaginabimur productas eſſe ad medium vſque pro-<lb/>pugnaculi ſiue valli eminentis, vt videre eſt in figura <lb/>ſequenti: </s> <s xml:id="echoid-s505" xml:space="preserve">Quòd ſi fortè voluiſſemus plateam primam <lb/>in totum apertam, dediſſemus ei quinquaginta pedes, <lb/>quum ei dederimus 20 pedes aperturæ. </s> <s xml:id="echoid-s506" xml:space="preserve">Statuendo e-<lb/>nim viginti pedes aperturæ, platea inferior habebit in <lb/>longitudinem pedes 50, vt ſuprà dictum eſt: </s> <s xml:id="echoid-s507" xml:space="preserve">quia 15 <lb/>pedes pro craſſitie pilæ, & </s> <s xml:id="echoid-s508" xml:space="preserve">alij 15 pedes ſub fornice <lb/>vltra pilam, cum 20 pedibus aperturæ, oſtendunt lon-<lb/>gitudinem dictæ plateæ eſſe 50 pedum: </s> <s xml:id="echoid-s509" xml:space="preserve">hæc autem <pb o="31" file="0031" n="39" rhead=""/> longicudo inſeruit retroceſſioni tormenti.</s> <s xml:id="echoid-s510" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s511" xml:space="preserve">Pila fit in medio duarum feneſtrarum tormentaria-<lb/>rum 20 pedes intra plateam inferiorem. </s> <s xml:id="echoid-s512" xml:space="preserve">Hæc autem <lb/>tam lata debet eſſe, vt tormenta queant commo-<lb/>dè retrocedere, vel ita componi, vt officio ſuo fun-<lb/>gi poſſint. </s> <s xml:id="echoid-s513" xml:space="preserve">Præterea latitudo plateæ inferioris tanta fit, <lb/>vt tormenta ei impoſita, & </s> <s xml:id="echoid-s514" xml:space="preserve">ad vſus neceſſarios accom-<lb/>modata, ſpatium retrocedendi habeant, ne impingant <lb/>ad muros latitudinis plateæ. </s> <s xml:id="echoid-s515" xml:space="preserve">Iam inſiſtentes iis quæ ſu-<lb/>prà dicta ſunt, & </s> <s xml:id="echoid-s516" xml:space="preserve">ſuper angulo <emph style="sc">ABC</emph> cupientes propu-<lb/>gnaculum noſtrum erigere, deſcriptionem noſtram ſe-<lb/>quendo, detrahemus à lineis <emph style="sc">AB</emph> & </s> <s xml:id="echoid-s517" xml:space="preserve"><emph style="sc">BC</emph> paſſus 25, vt ſu-<lb/>prà ſupputatum eſt, ſcilicet <emph style="sc">BD</emph> & </s> <s xml:id="echoid-s518" xml:space="preserve"><emph style="sc">BH</emph>, vt hîc in figura <lb/>apparet.</s> <s xml:id="echoid-s519" xml:space="preserve"/> </p> <figure> <image file="0031-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0031-01"/> </figure> <p> <s xml:id="echoid-s520" xml:space="preserve">Ad hæc, ſtatuemus latitudinem propugnaculi (la-<lb/>tus ſcilicet ipſius cum humero ſiue ſcapula, Galli di-<lb/>cunt cſpauſc,) 22 paſſuum: </s> <s xml:id="echoid-s521" xml:space="preserve">quæ latitudo hoc pacto de-<lb/>lineabitur: </s> <s xml:id="echoid-s522" xml:space="preserve">à punctis <emph style="sc">D</emph> & </s> <s xml:id="echoid-s523" xml:space="preserve"><emph style="sc">G</emph>, quæ propugnaculi angu-<lb/>los deſignant, ducemus duas lineas ad angulos rectos, <lb/>ſiue ad alios cujuſuis generis angulos, prout ſitui arcis <lb/>conuenit: </s> <s xml:id="echoid-s524" xml:space="preserve">verùm velimus eas nunc ad angulos rectos <pb o="32" file="0032" n="40" rhead=""/> ducere, prout in noſtra ſecunda operatione docui-<lb/>mus. </s> <s xml:id="echoid-s525" xml:space="preserve">Eruntq́; </s> <s xml:id="echoid-s526" xml:space="preserve">hæ duæ lineæ <emph style="sc">DE</emph> & </s> <s xml:id="echoid-s527" xml:space="preserve"><emph style="sc">GH</emph>, vt videre eſt in <lb/>figura.</s> <s xml:id="echoid-s528" xml:space="preserve"/> </p> <figure> <image file="0032-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0032-01"/> </figure> <p> <s xml:id="echoid-s529" xml:space="preserve">Has autem lineas <emph style="sc">DE</emph> & </s> <s xml:id="echoid-s530" xml:space="preserve"><emph style="sc">GH</emph>, vt ſuprà dictum eſt, fa-<lb/>ciemus 22 paſſuum pro latitudine laterum ac humero <lb/>rum propugnaculi. </s> <s xml:id="echoid-s531" xml:space="preserve">Ita præſcriptis menſuris longitu-<lb/>dinis & </s> <s xml:id="echoid-s532" xml:space="preserve">latitudinis propugnaculi, jam modum docea-<lb/>mus, qui obſeruari debet, ad erigendam frontem, ſeu <lb/>cortinam, vt hodie vocatur, propugnacúli. </s> <s xml:id="echoid-s533" xml:space="preserve">Primò, <lb/>neceſſariò dignoſcenda eſt longitudo totius cortinæ <lb/>inter duo propugnacula, ſiue inter propugnaculum, <lb/>& </s> <s xml:id="echoid-s534" xml:space="preserve">aliud quid quod volumus ab eo defendi. </s> <s xml:id="echoid-s535" xml:space="preserve">Verùm, <lb/>exempli gratia, ſtatuamus longitudinem eam eſſe inter <lb/>duo propugnacula, eſſeq́; </s> <s xml:id="echoid-s536" xml:space="preserve">lineam <emph style="sc">AD</emph>, longam paſſus <lb/>150. </s> <s xml:id="echoid-s537" xml:space="preserve">Angulum <emph style="sc">ABC</emph> diuidemus in duas partes æquales <lb/>per lineam <emph style="sc">FK</emph>, vt docet vltima primæ operationis fi-<lb/>gura.</s> <s xml:id="echoid-s538" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s539" xml:space="preserve">Præterea ſignabimus punctum <emph style="sc">I</emph> diſtans ab <emph style="sc">A</emph> pro <lb/>craſſitu dine lateris, & </s> <s xml:id="echoid-s540" xml:space="preserve">à puncto <emph style="sc">I</emph> ad punctum <emph style="sc">E</emph> lineam <lb/>rectam ducemus, quæ erit linea <emph style="sc">IE</emph>, quam produce-<lb/>mus quouſque ſecer lineam <emph style="sc">FK</emph> in puncto <emph style="sc">F</emph>: </s> <s xml:id="echoid-s541" xml:space="preserve">atque ita <pb o="33" file="0033" n="41" rhead=""/> linea <emph style="sc">EF</emph>, frontem propugnaculi deſignabit: </s> <s xml:id="echoid-s542" xml:space="preserve">à puncto <lb/>autem <emph style="sc">F</emph> ad punctum <emph style="sc">G</emph> ducetur linea <emph style="sc">FG</emph>, pro alia pro-<lb/>pugnaculi fronte: </s> <s xml:id="echoid-s543" xml:space="preserve">ſicq́ deſcriptum erit fun-<lb/>damentum <emph style="sc">DEFGHB</emph>, vt in proxi-<lb/>mè ſequenti figura <lb/>apparet.</s> <s xml:id="echoid-s544" xml:space="preserve"/> </p> <figure> <image file="0033-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0033-01"/> </figure> <pb o="34" file="0034" n="42" rhead=""/> <figure> <image file="0034-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0034-01"/> <caption xml:id="echoid-caption1" xml:space="preserve">PRI<gap/>FIGVRA.</caption> </figure> <pb file="0034_0035" n="43"/> <pb o="35" file="0035" n="44" rhead=""/> <figure> <image file="0035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0035-01"/> </figure> <pb file="0036" n="45"/> <pb o="37" file="0037" n="46" rhead=""/> <p> <s xml:id="echoid-s545" xml:space="preserve">Quòd ſi forſan duci non poſſet linea <emph style="sc">IE</emph> ad propu-<lb/>gnaculi frõtem deſignandam, nec ſuper ſolo, nec ſuper <lb/>charta, quòd neutrũ eorum ſatis capax eſſet ad eam ca <lb/>piendam, hoc modo procedemus. </s> <s xml:id="echoid-s546" xml:space="preserve">Statuendo lineam <lb/><emph style="sc">AD</emph>, cortinam ſcilicet inter duo propugnacula, eſſe paſ <lb/>ſuum 150, dicemus, ſi 157, (linea ſcilicet <emph style="sc">ID</emph>, quæ corti-<lb/>næ longitudinem complectitur, & </s> <s xml:id="echoid-s547" xml:space="preserve">lateris craſſitiem, <lb/>quæ eſt paſſuũ 7,) mihi dant in altitudinem paſſus 22, <lb/>lineam ſcilicet <emph style="sc">DE</emph>, quid mihi dabunt longitudo corti-<lb/>næ cum lateris ſpiſſitudine, & </s> <s xml:id="echoid-s548" xml:space="preserve">cum longitudine quæ <lb/>eſt ab angulo lateris ad angulum qui ambas cortinas <lb/>facit ductas à medio propugnaculi, paſſus ſcilicet 25 <lb/>cum 157, qui conjuncti, faciunt 182, lineam ſcilicet <lb/><emph style="sc">IB</emph>? </s> <s xml:id="echoid-s549" xml:space="preserve">Iam multiplico 182 cum 22, prodibunt 4004, quæ <lb/>4004 diuido per 157, prodeũt paſſus 25 cum dimidio: <lb/></s> <s xml:id="echoid-s550" xml:space="preserve">ac tanta erit linea <emph style="sc">BL</emph>, perpendicularis ducta ab angu-<lb/>lo, qui ambas cortinarum lineas facit, productas ad <lb/>medium propugnaculi in puncto <emph style="sc">B</emph>, vt videre eſt in ſu-<lb/>pradicta figura. </s> <s xml:id="echoid-s551" xml:space="preserve">A puncto autem <emph style="sc">E</emph> ad punctum <emph style="sc">L</emph>, li-<lb/>neam ducemus quæ ſecet lineam <emph style="sc">FK</emph> in puncto <emph style="sc">F</emph>: </s> <s xml:id="echoid-s552" xml:space="preserve">atq; </s> <s xml:id="echoid-s553" xml:space="preserve"><lb/>hac methodo propugnaculi frons formabitur, vt me-<lb/>liùs in figura declarabitur, in qua latitudo feneſtrarum <lb/>tormentariarum deſcribetur, pro prima propugnacu-<lb/>li platea. </s> <s xml:id="echoid-s554" xml:space="preserve">Fundamento in hunc modum deſignato, ei <lb/>addemus pro ſcamno duos vel tres pedes (Galli dicunt <lb/>zcſais, banquette: </s> <s xml:id="echoid-s555" xml:space="preserve">eſt autem ſpatiolum id, quo plus patet <lb/>fundamentum quàm murus ei impoſitus) ducendo li-<lb/>neam æquidiſtantem circa fundamentum duobus pe-<lb/>dibus, vel duobus cum dimidio ab initio muri diſtan-<lb/>tem. </s> <s xml:id="echoid-s556" xml:space="preserve">Hoc autem ſpatio minimum dari non poteſt: </s> <s xml:id="echoid-s557" xml:space="preserve">vt <lb/>apparet in ſecunda figura ſequente <emph style="sc">IKLMN</emph>.</s> <s xml:id="echoid-s558" xml:space="preserve"/> </p> <pb o="38" file="0038" n="47" rhead=""/> <figure> <image file="0038-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0038-01"/> </figure> </div> <div xml:id="echoid-div27" type="section" level="1" n="24"> <head xml:id="echoid-head29" xml:space="preserve">SECVN<gap/>FIGVRA.</head> <pb file="0038a" n="48"/> <figure> <image file="0038a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0038a-01"/> </figure> <pb file="0038_0039" n="49"/> <pb o="39" file="0039" n="50" rhead=""/> <figure> <image file="0039-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0039-01"/> </figure> <pb o="40" file="0040" n="51" rhead=""/> <p> <s xml:id="echoid-s559" xml:space="preserve">Debemus autem diligenter conſiderare deſcriptio-<lb/>nem hanc fundamenti propugnaculi, quia ſecundùm <lb/>eam poterunt deſcribi propugnacula cum vna pla-<lb/>tea, cum duabus, cum tribus, & </s> <s xml:id="echoid-s560" xml:space="preserve">quouis alio modo pla-<lb/>cuerit, nec periculum erit quòd architectus opere fi-<lb/>nito ſentiat, ſed ſerò, ſe à propoſito ſcopo aberraſſe. </s> <s xml:id="echoid-s561" xml:space="preserve">Ha-<lb/>bita longitudine & </s> <s xml:id="echoid-s562" xml:space="preserve">latitudine fundamenti cum ſuo <lb/>ſcamno, maturè perpendetur, an ſolum aptum ſit ad <lb/>propugnaculum ſuſtinendum, ita vt nulla labes ob <lb/>fundamenti defectum conſequatur. </s> <s xml:id="echoid-s563" xml:space="preserve">Non abs re igi-<lb/>tur erit, de qualitate fundamentorum diſſerere. </s> <s xml:id="echoid-s564" xml:space="preserve">At <lb/>quoniam fundamenta jaciuntur aliàs in ſolo hujus ge-<lb/>neris, aliàs in alîus, diſtinguenda nobis primùm e-<lb/>runt: </s> <s xml:id="echoid-s565" xml:space="preserve">ac primò de vno genere dicemus, deinde de <lb/>aliis.</s> <s xml:id="echoid-s566" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div28" type="section" level="1" n="25"> <head xml:id="echoid-head30" xml:space="preserve">PRIMVS MODVS.</head> <p> <s xml:id="echoid-s567" xml:space="preserve">Si jaciendum nobis ſit fundamentum in loco ſic-<lb/>co, fodietur ſolum à quinque in ſex pedes, plus vel <lb/>minus, prout videbitur ſatis eſſe, explanando appri-<lb/>me fundum, ita tamen vt explanatio illa pauliſper <lb/>pendeat centrum verſus. </s> <s xml:id="echoid-s568" xml:space="preserve">Deinde, in planitie hujuſce <lb/>effoſſionis palatio fieri debet hoc modo. </s> <s xml:id="echoid-s569" xml:space="preserve">Primò ſume-<lb/>tur palus longior multo quàm par ſit, in h ócque palo <lb/>ſignabuntur pedes & </s> <s xml:id="echoid-s570" xml:space="preserve">digiti, ſicut in orgyia ſeu regula <lb/>menſoria: </s> <s xml:id="echoid-s571" xml:space="preserve">hoc facto adigetur fiſtucâ palus hic in fun-<lb/>dum ipſius planitiei, quantum adigi poterit, ex eoq́; <lb/></s> <s xml:id="echoid-s572" xml:space="preserve">ita adacto dignoſcetur, quàm longi debeant eſſe pali, <lb/>qui ea menſura fient ad quam vſque potuit primus <lb/>terræ infigi. </s> <s xml:id="echoid-s573" xml:space="preserve">Lignum autem magis ad hanc rem & </s> <s xml:id="echoid-s574" xml:space="preserve">ad <lb/>alias noſtræ huic profeſſioni neceſſarias commodum, <lb/>erit quercus, alnus, caſtanea: </s> <s xml:id="echoid-s575" xml:space="preserve">verùm ex his alnus me- <pb o="41" file="0041" n="52" rhead=""/> lior mihi videtur. </s> <s xml:id="echoid-s576" xml:space="preserve">Fiet ita hæc palatio, vt palus vnus ab <lb/>alio pede dimidio diſter, plus vel minus, pro ſoli boni-<lb/>tate. </s> <s xml:id="echoid-s577" xml:space="preserve">Debent autem ſic æquari hi pali cum ſolo, vt ex <lb/>ambobus vnica ſuperficies, eaq́ planiſſima, fiat, vt vi-<lb/>dere eſt in ſequenti figura in parte <emph style="sc">A</emph>. </s> <s xml:id="echoid-s578" xml:space="preserve">Hac æquatione <lb/>facta, denuò eruetur tantum terræ per totam palatio-<lb/>nem, vt pali ſupra terram dimidiato pede emineant, vt <lb/>apparet in ſequenti figura in parte <emph style="sc">B</emph>, idq́ vt in locum <lb/>terræ erutæ, fiſtucâ adigantur optima ſaxa, cruſtam <lb/>facientia benè æquatam, centrum verſus tamen, vt <lb/>ſuprà dictum eſt, pendentem. </s> <s xml:id="echoid-s579" xml:space="preserve">Hic autem mo-<lb/>dus apparet in tertia ſequenti figura in <lb/>parte <emph style="sc">C</emph>. </s> <s xml:id="echoid-s580" xml:space="preserve">Atque ita conſtrue-<lb/>tur fundamentum.</s> <s xml:id="echoid-s581" xml:space="preserve"/> </p> <figure> <image file="0041-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0041-01"/> </figure> <figure> <image file="0041-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0041-02"/> </figure> <pb o="42" file="0042" n="53" rhead=""/> <figure> <image file="0042-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0042-01"/> <caption xml:id="echoid-caption2" xml:space="preserve">TERTIA <gap/>VRA.</caption> </figure> <pb file="0042_0043" n="54"/> <pb o="43" file="0043" n="55" rhead=""/> <figure> <image file="0043-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0043-01"/> </figure> <pb file="0044" n="56"/> <pb o="45" file="0045" n="57" rhead=""/> <p> <s xml:id="echoid-s582" xml:space="preserve">Hac palatione per totum fundamentum facta, eaq́; <lb/></s> <s xml:id="echoid-s583" xml:space="preserve">ſaxis, vt diximus, munita, inædificabimus optimum <lb/>murum, pro capacitate ipſius fundamenti, ſemipe-<lb/>de altiorem terreno viæ ſupernæ, quia propter immen-<lb/>ſum pondus, fundamentum aliquanto deprimitur. </s> <s xml:id="echoid-s584" xml:space="preserve">De-<lb/>bet autem hic murus, qui ad viam vſque ſupernam, <lb/>bene æquari, ea lege tamen vt centrum verſus pen-<lb/>deat, vt & </s> <s xml:id="echoid-s585" xml:space="preserve">ſuprà dictum eſt, beneq́; </s> <s xml:id="echoid-s586" xml:space="preserve">obſeruatis longitu-<lb/>dinibus & </s> <s xml:id="echoid-s587" xml:space="preserve">latitudinibus neceſſariis. </s> <s xml:id="echoid-s588" xml:space="preserve">Fundamentum <lb/>verò, cum ſua palatione, ad minus pedes duos <lb/>vel tres latius eſſe debet, quàm conſtru-<lb/>ctio propugnaculi vel fabricæ, <lb/>vt videre eſt in ſequenti <lb/>quarta figura.</s> <s xml:id="echoid-s589" xml:space="preserve"/> </p> <figure> <image file="0045-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0045-01"/> </figure> <pb o="46" file="0046" n="58" rhead=""/> <figure> <image file="0046-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0046-01"/> <caption xml:id="echoid-caption3" xml:space="preserve">QV<gap/>A FIGVRA.</caption> </figure> <pb file="0046_0047" n="59"/> <pb o="47" file="0047" n="60" rhead=""/> <figure> <image file="0047-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0047-01"/> </figure> <pb file="0048" n="61"/> <pb o="49" file="0049" n="62" rhead=""/> </div> <div xml:id="echoid-div29" type="section" level="1" n="26"> <head xml:id="echoid-head31" xml:space="preserve">SECVNDVS MODVS.</head> <p> <s xml:id="echoid-s590" xml:space="preserve">Si jaciendum eſſet fundamentum ſupra ſolum are-<lb/>noſum, ſabuloſum, vel glareoſum, effodietur terra ad <lb/>octo vel decem pedes, plus minus, prout ex vſu eſſe <lb/>videbitur: </s> <s xml:id="echoid-s591" xml:space="preserve">& </s> <s xml:id="echoid-s592" xml:space="preserve">explanato fundo, vt ſuprà, quia inibi pa-<lb/>latio fieri non poteſt, fiet contignatio ex duobus aut <lb/>tribus lignis inſimul alligatis, necnon & </s> <s xml:id="echoid-s593" xml:space="preserve">ex bonis tra-<lb/>bibus bene & </s> <s xml:id="echoid-s594" xml:space="preserve">ad perpendiculum cum fundo æquatis, <lb/>ea tamen lege, vt ſemper pendeat paululum hæc con-<lb/>tignatio centrum verſus, ſintq́; </s> <s xml:id="echoid-s595" xml:space="preserve">hæ trabes benè inter ſe <lb/>colligatæ, & </s> <s xml:id="echoid-s596" xml:space="preserve">junctæ vna ad aliam, vt apparet in altera <lb/>parte quintæ figuræ. </s> <s xml:id="echoid-s597" xml:space="preserve">Super hanc autem con-<lb/>tignationem conſtruetur murus, <lb/>vt docet ſecunda primi <lb/>modi figura.</s> <s xml:id="echoid-s598" xml:space="preserve"/> </p> <figure> <image file="0049-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0049-01"/> </figure> <pb o="50" file="0050" n="63" rhead=""/> <figure> <image file="0050-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0050-01"/> <caption xml:id="echoid-caption4" xml:space="preserve">QVINTA<gap/>GVRA.</caption> </figure> <pb file="0050_0051" n="64"/> <pb o="51" file="0051" n="65" rhead=""/> <figure> <image file="0051-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0051-01"/> </figure> <pb o="52" file="0052" n="66" rhead=""/> </div> <div xml:id="echoid-div30" type="section" level="1" n="27"> <head xml:id="echoid-head32" xml:space="preserve">TERTIVS MODVS.</head> <p> <s xml:id="echoid-s599" xml:space="preserve">Si fundamentum jaciendum eſt vbi ſolum eſſet <lb/>molle, vt ſunt paludes, vel circa flumen, lacum, mare, <lb/>& </s> <s xml:id="echoid-s600" xml:space="preserve">ſimilia, effodietur terra quantum ſatis erit, & </s> <s xml:id="echoid-s601" xml:space="preserve">ex-<lb/>æquabitur vt ſuprà ſolum, fietq̀; </s> <s xml:id="echoid-s602" xml:space="preserve">palatio cum ſu-<lb/>blicis, altera è regione alterius, deinde eruetur terra, <lb/>vt ſuprà factum eſt in figura primi modi in parte <emph style="sc">B</emph>, ita <lb/>tamen vt plus emineant pali quàm in primo mo-<lb/>do, vt poſſint inſeri trabes in tranſuerſum, inſimul <lb/>bene impagibus ſeu clauis ligneis alligatæ, in modum <lb/>feneſtræ clathratæ. </s> <s xml:id="echoid-s603" xml:space="preserve">Præterea fiet cruſta inter palum <lb/>& </s> <s xml:id="echoid-s604" xml:space="preserve">palum, ſicut in primo modo: </s> <s xml:id="echoid-s605" xml:space="preserve">& </s> <s xml:id="echoid-s606" xml:space="preserve">ſuper hac cruſta <lb/>fiet contignatio eadem quæ facta fuit ſuper fundo ſe-<lb/>cundi modi, & </s> <s xml:id="echoid-s607" xml:space="preserve">tandem ſuper hac contigna-<lb/>tione conſtruetur optimus murus, <lb/>ſicut in ſecunda figura <lb/>primi modi.</s> <s xml:id="echoid-s608" xml:space="preserve"/> </p> <figure> <image file="0052-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0052-01"/> </figure> <pb o="53" file="0053" n="67" rhead=""/> </div> <div xml:id="echoid-div31" type="section" level="1" n="28"> <head xml:id="echoid-head33" xml:space="preserve">QVARTVS MODVS.</head> <p> <s xml:id="echoid-s609" xml:space="preserve">Si jaciendum eſſet fundamentum in loco partim ſa-<lb/>xoſo, partim verò terreo, ita vt commodè non poſſent <lb/>adigi pali, effo diendum eſt in profundum ad decem <lb/>vel duodecim pedes, plus minus, prout neceſſarium <lb/>videbitur, & </s> <s xml:id="echoid-s610" xml:space="preserve">curare vt fundus ſit exactè adæquatus ad <lb/>perpendiculum: </s> <s xml:id="echoid-s611" xml:space="preserve">quo facto, palationis loco fient tot <lb/>pilæ lapideæ, quot angulos habebit propugnacu-<lb/>lum, vel prout erit neceſſe, pro frontium & </s> <s xml:id="echoid-s612" xml:space="preserve">laterum <lb/>propugnaculi lognitudine. </s> <s xml:id="echoid-s613" xml:space="preserve">Deinde ab vna pila ad a-<lb/>liam fiet fornix cum duplici arcu, altero ſupra al-<lb/>terum, ita vt conuexitas vnius conuexi-<lb/>tatem alterius reſpiciat, ſicut <lb/>apparet in ſexta figu-<lb/>ra ſequenti.</s> <s xml:id="echoid-s614" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div32" type="section" level="1" n="29"> <head xml:id="echoid-head34" xml:space="preserve">QVINTVS MODVS.</head> <p> <s xml:id="echoid-s615" xml:space="preserve">Occurrit etiã aliquãdo, vt fabricãdũ ſit in loco, qui <lb/>fundamento non egeat: </s> <s xml:id="echoid-s616" xml:space="preserve">vt accidit in ſolo quod eſt ex <lb/>viuo & </s> <s xml:id="echoid-s617" xml:space="preserve">ſolido faxo: </s> <s xml:id="echoid-s618" xml:space="preserve">tunc adæquandum eſt exactè ſo-<lb/>lum, ita tamen vt paululum pendeat centrum verſus, <lb/>vt ſuprà dictum eſt. </s> <s xml:id="echoid-s619" xml:space="preserve">Quòd ſi ſaxum eſſet mótuoſum, <lb/>paulatim exſcindetur in modum graduú: </s> <s xml:id="echoid-s620" xml:space="preserve">qui quidem <lb/>gradus ſint benè adæquati, pendeant tamen paululum <lb/>centrum verſus: </s> <s xml:id="echoid-s621" xml:space="preserve">vt jam ſæpe dictum eſt. </s> <s xml:id="echoid-s622" xml:space="preserve">Quo facto, <lb/>propugnaculum, quod inſtituimus exſtruere, ſuperæ-<lb/>dificabitur, obſeruatis longitudine & </s> <s xml:id="echoid-s623" xml:space="preserve">latitudine ipſi <lb/>neceſſariis.</s> <s xml:id="echoid-s624" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s625" xml:space="preserve">Deſignatis & </s> <s xml:id="echoid-s626" xml:space="preserve">bene adæquatis fundamentis ſuper-<lb/>nè, ita tamen vt paululum declinent centrum verſus, <pb o="54" file="0054" n="68" rhead=""/> <pb file="0054_0055" n="69"/> <pb o="55" file="0055" n="70" rhead=""/> <anchor type="figure" xlink:label="fig-0055-01a" xlink:href="fig-0055-01"/> <pb o="56" file="0056" n="71" rhead=""/> deſcribemus ſigillatim reliqua omnia noſtri propu- gnaculi, quæ huic fundamento bene adæquato ſuper- ædificari debent. </s> <s xml:id="echoid-s627" xml:space="preserve">Statuamus igitur deſcribendum id nobis eſſe ſuper vno ex præfatis fundamentis, primò deſignabimus ſcamnum, (Galli dicunt vcfais ou ban- qucttc) fundamenti propugnaculi, inclinationem mu- ri, murum ipſum, cuniculum tranſuerſum, & </s> <s xml:id="echoid-s628" xml:space="preserve">ipſius cuniculi murum: </s> <s xml:id="echoid-s629" xml:space="preserve">murum autem hunc nolo vt exce- dat cuniculum tranſuerſum: </s> <s xml:id="echoid-s630" xml:space="preserve">cuniculum verò altiorem nolo eſſe quinque vel ſex pedum, ſuper quo extruetur fornix. </s> <s xml:id="echoid-s631" xml:space="preserve">Hæc omnia extruétur circum propugnaculum, & </s> <s xml:id="echoid-s632" xml:space="preserve">ad ipſam cortinam: </s> <s xml:id="echoid-s633" xml:space="preserve">cujus quidem cortinæ licet ſu- prà nulla vel ſaltem rara mentio facta fuit, ſatis tamen notum eſt arces ſeu caſtra non poſſe exſtrui abſque his cortinis: </s> <s xml:id="echoid-s634" xml:space="preserve">ſunt enim hæ ipſamet diſtantia à propu- gnaculo, ſeu vallo eminenti, ad propugnaculum. </s> <s xml:id="echoid-s635" xml:space="preserve">His deſcriptis deſignabuntur anterides ſeu eriſmata, (Galli dicunt cſpcrons ou contrcforts) quæ ſunt circum propu- gnaculum & </s> <s xml:id="echoid-s636" xml:space="preserve">ad ipſam cortinam. </s> <s xml:id="echoid-s637" xml:space="preserve">Hæ autem anterides eo longiores ſunt à cuniculo tranſuerſo in ſuprà, quan- ta eſt cuniculi tranſuerſi cum ſuo muro latitudo: </s> <s xml:id="echoid-s638" xml:space="preserve">ante- rides verò humeri eouſque producuntur, quo finit primæ plateæ latitudo. </s> <s xml:id="echoid-s639" xml:space="preserve">Hæc verò latitudo quatuor aut quinque pedibus æqualiter diſtatà rettoceſſione bom- bardarum ſecundæ feneſtræ tormentariæ primæ pla- teæ, dum ita ſitæ ſunt dictæ bombardæ, vt colliman- do rectà poſſint ferire ad medium vſque ipſius corti- næ. </s> <s xml:id="echoid-s640" xml:space="preserve">Galli dicunt, portce dc bfanc cy bfanc. </s> <s xml:id="echoid-s641" xml:space="preserve">Anterides frontis propugnaculi ad minus debent æquipollere duabus tertiis earum quæ ſunt ad humerum: </s> <s xml:id="echoid-s642" xml:space="preserve">anteri- des lateris habent in longitudine dimidium anteri- <pb o="57" file="0057" n="72" rhead=""/> dum humeri: </s> <s xml:id="echoid-s643" xml:space="preserve">& </s> <s xml:id="echoid-s644" xml:space="preserve">anterides cortinæ æquipollent dua- bus tertiis earum quæ ad latus: </s> <s xml:id="echoid-s645" xml:space="preserve">debentq́; </s> <s xml:id="echoid-s646" xml:space="preserve">ita deſignari, vt duobus aut tribus pedibus longiores & </s> <s xml:id="echoid-s647" xml:space="preserve">latiores ſint iis quæ deſignabuntur ſupra primam plateam: </s> <s xml:id="echoid-s648" xml:space="preserve">intere- ritq́; </s> <s xml:id="echoid-s649" xml:space="preserve">inter eas ſpatium decem vel duodecim pedum.</s> <s xml:id="echoid-s650" xml:space="preserve"> Præterea hæ omnes menſuræ augeſcent aut minuen- tur pro ſitus varietate, & </s> <s xml:id="echoid-s651" xml:space="preserve">habita ratione impenſarum quas in iis facere voluerimus. </s> <s xml:id="echoid-s652" xml:space="preserve">Deſignatis ſupradictis anteridibus, deſignabuntur pilæ lapideæ intus quan- tum ſtatuetur primas plateas apertas eſſe: </s> <s xml:id="echoid-s653" xml:space="preserve">deſignabun- turq́; </s> <s xml:id="echoid-s654" xml:space="preserve">intra primas plateas 20 pedes, vt ſuprà dictum eſt, duobus aut tribus pedibus longiores & </s> <s xml:id="echoid-s655" xml:space="preserve">latiores quàm eæ quæ ſupra primas plateas: </s> <s xml:id="echoid-s656" xml:space="preserve">eaq́ lege deſcri- bentur, vt quum fabricatæ fuerint aduſque primas plateas, & </s> <s xml:id="echoid-s657" xml:space="preserve">à primis aduſque ſecundas, bombardæ pri- mæ plateæ non impingant in dictas pilas. </s> <s xml:id="echoid-s658" xml:space="preserve">Deſignatis pilis deſignabuntur alæ propugnaculi, ea conditione vt quum fabricatæ fuerint aduſque primas plateas &</s> <s xml:id="echoid-s659" xml:space="preserve"> fupra eas, æquè diſtent quatuor aut quinque pedibus à retroceſſionibus bombardarum, quæ ſunt in pri- mis plateis, quæ ſcilicet ſunt in duabus primis feneſtris tormentariis: </s> <s xml:id="echoid-s660" xml:space="preserve">quia ſi retrocedendo bombardæ in mu- ros impingerent, compactio illa lignea, cui innitun- tur, (Galli vocant attcſagc) omnino frangeretur ac diſ- ſolueretur. </s> <s xml:id="echoid-s661" xml:space="preserve">Præterea deſignabitur murus ſpiſſitu dinis octo aut decem pedum, qui longitudinem primarum platearum terminabit. </s> <s xml:id="echoid-s662" xml:space="preserve">Hæc autem omnia apparent deſignata in ſequenti ſeptima figura, vt indicant litte- ræ ſequentes.</s> <s xml:id="echoid-s663" xml:space="preserve"/> </p> <div xml:id="echoid-div32" type="float" level="2" n="1"> <figure xlink:label="fig-0054-01" xlink:href="fig-0054-01a"> <image file="0054-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0054-01"/> </figure> <figure xlink:label="fig-0055-01" xlink:href="fig-0055-01a"> <image file="0055-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0055-01"/> </figure> </div> <pb o="58" file="0058" n="73" rhead=""/> <figure> <image file="0058-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0058-01"/> <caption xml:id="echoid-caption5" xml:space="preserve">SEPTIM<gap/>GVRA.</caption> </figure> <pb file="0058_0059" n="74"/> <pb o="59" file="0059" n="75" rhead=""/> <figure> <image file="0059-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0059-01"/> </figure> <pb o="60" file="0060" n="76" rhead=""/> <p> <s xml:id="echoid-s664" xml:space="preserve"><emph style="sc">A</emph> Scamnum fundamenti. </s> <s xml:id="echoid-s665" xml:space="preserve">Galli dicunt zefais ou ban-<lb/>quette.</s> <s xml:id="echoid-s666" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s667" xml:space="preserve"><emph style="sc">B</emph> Inclinatio muri. </s> <s xml:id="echoid-s668" xml:space="preserve">Galli dicunt efcarpe.</s> <s xml:id="echoid-s669" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s670" xml:space="preserve"><emph style="sc">C</emph> Murus.</s> <s xml:id="echoid-s671" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s672" xml:space="preserve"><emph style="sc">D</emph> Cuniculus tranſuerſus.</s> <s xml:id="echoid-s673" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s674" xml:space="preserve"><emph style="sc">E</emph> Murus cuniculi tranſuerſi.</s> <s xml:id="echoid-s675" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s676" xml:space="preserve"><emph style="sc">F</emph> Anterides lateris. </s> <s xml:id="echoid-s677" xml:space="preserve">Galli vocant eſpezon@ ou contrefozts.</s> <s xml:id="echoid-s678" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s679" xml:space="preserve"><emph style="sc">G</emph> Pila lapidea.</s> <s xml:id="echoid-s680" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s681" xml:space="preserve"><emph style="sc">H</emph> Murus qui ſuſtinet terram & </s> <s xml:id="echoid-s682" xml:space="preserve">fornices plateæ ſupe-<lb/>rioris.</s> <s xml:id="echoid-s683" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s684" xml:space="preserve"><emph style="sc">I</emph> Anterides humeri propugnaculi.</s> <s xml:id="echoid-s685" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s686" xml:space="preserve"><emph style="sc">K</emph> Anterides frontis propugnaculi.</s> <s xml:id="echoid-s687" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s688" xml:space="preserve"><emph style="sc">L</emph> Anterides cortinæ.</s> <s xml:id="echoid-s689" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s690" xml:space="preserve"><emph style="sc">M</emph> Ala propugnaculi.</s> <s xml:id="echoid-s691" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s692" xml:space="preserve"><emph style="sc">O</emph> Fundamentum quod duobus aut tribus pedibus <lb/>fabricam intrinſecam exuperat.</s> <s xml:id="echoid-s693" xml:space="preserve"/> </p> <figure> <image file="0060-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0060-01"/> </figure> <pb o="61" file="0061" n="77" rhead=""/> <p> <s xml:id="echoid-s694" xml:space="preserve">Deſignatis ſupradictis omnibus, accedemus ad fa-<lb/>bricam, dantes ſingulis quinis pedibus aſcenſus pe-<lb/>dem vnum inclinationis extrinſecus, vt ſuprſa4; <lb/></s> <s xml:id="echoid-s695" xml:space="preserve">diximus, idq́; </s> <s xml:id="echoid-s696" xml:space="preserve">vſque ad altitudinem prima-<lb/>rum platearum, vt meliùs com-<lb/>prehendipoteſt in octaua <lb/>ſequenti figura.</s> <s xml:id="echoid-s697" xml:space="preserve"/> </p> <figure> <image file="0061-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0061-01"/> </figure> <pb o="62" file="0062" n="78" rhead=""/> <figure> <image file="0062-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0062-01"/> <caption xml:id="echoid-caption6" xml:space="preserve">OCTAVA<gap/>GVRA.</caption> </figure> <pb file="0062_0063" n="79"/> <pb o="63" file="0063" n="80" rhead=""/> <figure> <image file="0063-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0063-01"/> </figure> <pb o="64" file="0064" n="81" rhead=""/> <p> <s xml:id="echoid-s698" xml:space="preserve">Præterea ad altitudinem vſque primarum platea-<lb/>rum, replebitur vacuum optima terra & </s> <s xml:id="echoid-s699" xml:space="preserve">ſaxis, dein-<lb/>de adæquabitur ſolum, paululum vergens centrum ver <lb/>ſus. </s> <s xml:id="echoid-s700" xml:space="preserve">Hoc facto, ſuper eadem fabrica, quæ aduſque <lb/>primas plateas facta eſt, denuò deſignabuntur eadem <lb/>quæ priùs, detrahendo intrinſecus pedem vnum vel <lb/>duos à longitudine & </s> <s xml:id="echoid-s701" xml:space="preserve">latitudine, vt ſuprà dictum eſt, <lb/>cum ſuis anteridibus. </s> <s xml:id="echoid-s702" xml:space="preserve">Anterides autem quatuor poſ-<lb/>ſunt deſignari modis ſuper fabrica, latiores ſcilicet ar-<lb/>cem verſus: </s> <s xml:id="echoid-s703" xml:space="preserve">vel ejuſdem latitudinis in capitibus, ſtri-<lb/>ctiores verò circa medium: </s> <s xml:id="echoid-s704" xml:space="preserve">vel capitibus æqualibus, <lb/>latiores autem in medio, ad oui formam: </s> <s xml:id="echoid-s705" xml:space="preserve">vel ſtrictio-<lb/>res arcem verſus. </s> <s xml:id="echoid-s706" xml:space="preserve">In noſtris deſcriptionibus, duos tan-<lb/>tùm ex illis quatuor vſurpauimus: </s> <s xml:id="echoid-s707" xml:space="preserve">ſtrictiores ſcilicet <lb/>arcem verſus, & </s> <s xml:id="echoid-s708" xml:space="preserve">latiores arcem verſus, vt in noſtris <lb/>delineationibus apparet. </s> <s xml:id="echoid-s709" xml:space="preserve">Ex his autem meliores ſunt <lb/>eæ quæ latiores ſunt arcẽ verſus: </s> <s xml:id="echoid-s710" xml:space="preserve">poſt has verò eæ quæ <lb/>quum capita æqualia habeant, circa medium ſtrictio-<lb/>res ſunt. </s> <s xml:id="echoid-s711" xml:space="preserve">Hæc enim duo genera meliùs reſiſtunt ho-<lb/>ſtium oppugnationi, nec tam facile fabrica periculum <lb/>ruinæ incurrit, nec foſſa arcis tam citò impletur. </s> <s xml:id="echoid-s712" xml:space="preserve">In <lb/>hunc modum anteridibus deſignatis, deſignabitur via, <lb/>per quam ab vna platea ad aliam eatur, fietq́; </s> <s xml:id="echoid-s713" xml:space="preserve">ita pla-<lb/>nities ambarum platearum, vt paululum declinet ver-<lb/>ſus feneſtras tormentarias, vt faciliùs poſſint bombar-<lb/>dæ conduci ad ipſas feneſtras. </s> <s xml:id="echoid-s714" xml:space="preserve">Deſignabuntur præterea <lb/>duæ viæ, quibus ad duas plateas eatur. </s> <s xml:id="echoid-s715" xml:space="preserve">His omnibus <lb/>fabricatis, dabitur modus auriculas conſtruendi, (Gal-<lb/>li dicunt orciſſons.) </s> <s xml:id="echoid-s716" xml:space="preserve">Producuntur verò hæ auriculæ <lb/>tanto extrinſecus, vt feneſtræ tormentariæ non poſ-<lb/>ſint inſpici à jugo aliquo extrinſeco ſeu aggere emi- <pb o="65" file="0065" n="82" rhead=""/> nenti: </s> <s xml:id="echoid-s717" xml:space="preserve">fiuntq́; </s> <s xml:id="echoid-s718" xml:space="preserve">abſque vlla muri inclinatione à parte <lb/>feneſtrarum, vt videre eſt in noſtris deſcriptionibus. <lb/></s> <s xml:id="echoid-s719" xml:space="preserve">conſtruuntur autem variis modis, fronte ſcilicet cir-<lb/>cinata, vel quadrata, vel obliqua, de quibus tamen <lb/>hucuſque nulla à nobis facta fuit mentio. </s> <s xml:id="echoid-s720" xml:space="preserve">Ad fabri-<lb/>candas haſce auriculas, producentur duæ lineæ, ea <lb/>ſcilicet quæ terminat extrinſecam latitudinem viæ ſe-<lb/>cundæ feneſtræ tormentariæ, humerum verſus (hujus <lb/>autem lineæ mentio fiet in vndecima figura,) altera <lb/>verò quæ frontem propugnaculi delineat. </s> <s xml:id="echoid-s721" xml:space="preserve">Hæ lineæ <lb/>producentur quouſque protendi voluerimus noſtram <lb/>auriculam. </s> <s xml:id="echoid-s722" xml:space="preserve">Quòd ſi obliquam auriculam voluerimus, <lb/>altera ex illis lineis longiùs producetur. </s> <s xml:id="echoid-s723" xml:space="preserve">Si quadratam <lb/>vel circinatam nobis eam placeat eſſe, æqualiter pro-<lb/>ducentur, vt in ſequenti nona figura apparet.</s> <s xml:id="echoid-s724" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s725" xml:space="preserve"><emph style="sc">T</emph> Viæ, per quas ad plateas inferiores itur.</s> <s xml:id="echoid-s726" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s727" xml:space="preserve"><emph style="sc">V</emph> Via, quæ ab vna platea ad aliam tendit.</s> <s xml:id="echoid-s728" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s729" xml:space="preserve"><emph style="sc">X</emph> Auricula propugnaculi.</s> <s xml:id="echoid-s730" xml:space="preserve"/> </p> <figure> <image file="0065-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0065-01"/> </figure> <pb o="66" file="0066" n="83" rhead=""/> <figure> <image file="0066-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0066-01"/> <caption xml:id="echoid-caption7" xml:space="preserve">NONA<gap/>GVRA.</caption> </figure> <pb file="0066_0067" n="84"/> <pb o="67" file="0067" n="85" rhead=""/> <figure> <image file="0067-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0067-01"/> </figure> <pb o="68" file="0068" n="86" rhead=""/> <p> <s xml:id="echoid-s731" xml:space="preserve">Super his plateis deſignabuntur feneſtræ tormen-<lb/>tariæ, in eum modum vt foſſam verſus pendeant, ita <lb/>vt ij qui intra plateam ſunt, ad minus poſſint medium <lb/>ipſius foſſæ vndequaque intueri: </s> <s xml:id="echoid-s732" xml:space="preserve">deſignentur etiam <lb/>ita, vt bombardæ poſſint officio ſuo fungi ad arcis <lb/>defenſionem. </s> <s xml:id="echoid-s733" xml:space="preserve">In his autem noſtris deſcriptionibus, <lb/>deſignemus duas feneſtras tormentarias pro vnaqua-<lb/>que platea inferiori. </s> <s xml:id="echoid-s734" xml:space="preserve">Prima ab angulo lateris diſtabit <lb/>pedibus duobus vel tribus, ita vt bombardæ poſſint <lb/>euerrere hoſtium per ſcalas aſcenſus in arcis cortinam. <lb/></s> <s xml:id="echoid-s735" xml:space="preserve">Latitudines autem extrinſecas earum feneſtrarum, ſta-<lb/>tuemus eſſe pedes 9 pro prima, pro ſecunda verò 8. </s> <s xml:id="echoid-s736" xml:space="preserve"><lb/>Pinnam intermediam (Galli dicunt Mcrſoy,) pedes <lb/>30 latam faciemus. </s> <s xml:id="echoid-s737" xml:space="preserve">Latitudines intrinſecæ earum fe-<lb/>neſtrarum erunt pedum 5: </s> <s xml:id="echoid-s738" xml:space="preserve">intro verò pro longitudi-<lb/>ne pedes 3: </s> <s xml:id="echoid-s739" xml:space="preserve">vbi autem ſtrictiores ſunt eæ feneſtræ, pro <lb/>latitudine pedes 3. </s> <s xml:id="echoid-s740" xml:space="preserve">Quæ latitudines intrinſecæ & </s> <s xml:id="echoid-s741" xml:space="preserve">ex-<lb/>trinſecæ tormentariarum feneſtrarum ita componun-<lb/>tur, vt primæ feneſtræ bombardæ inſeruiant ad euer-<lb/>rendum aggerem extrinſecum (Galli dicunt contreſcaz-<lb/>pc,) frontem propugnaculi, & </s> <s xml:id="echoid-s742" xml:space="preserve">integram foſſam, aduſ-<lb/>que cortinam, vt docẽt lineæ K L, K M, & </s> <s xml:id="echoid-s743" xml:space="preserve">K N decimæ ſe-<lb/>quentis figuræ. </s> <s xml:id="echoid-s744" xml:space="preserve">Bombardis ſecundæ feneſtræ incum-<lb/>bet euerrere foſſulam quæ fit in medio magnæ foſſæ, <lb/>quando ita deſignatur, vt in ea debeat eſſe aqua per-<lb/>ennis: </s> <s xml:id="echoid-s745" xml:space="preserve">cujus foſſulæ latitudo fit vt plurimum quin-<lb/>decim pedum vel circa, altitudo verò ſeptem cum di-<lb/>midio. </s> <s xml:id="echoid-s746" xml:space="preserve">Quòd ſi inibi aqua non eſſet, cuperem vt ita <lb/>aptata eſſet feneſtra tormentaria, vt ejus bombardæ, <lb/>quantum poſſent, angulum propugnaculi euerre-<lb/>rent, & </s> <s xml:id="echoid-s747" xml:space="preserve">ab hinc introrſum, ita vt collimando rectà <pb o="69" file="0069" n="87" rhead=""/> poſſint ferire cortinæ dimidium, vt docent lineæ <emph style="sc">O P</emph>, <lb/><emph style="sc">O Q</emph>, & </s> <s xml:id="echoid-s748" xml:space="preserve"><emph style="sc">O D</emph> decimæ ſequentis figuræ. </s> <s xml:id="echoid-s749" xml:space="preserve">Attamen in par-<lb/>te extrinſeca feneſtrarum vellem eſſe gradus ſeu ſcalas <lb/>lapideas intrò pedum quinque in longitudinem: </s> <s xml:id="echoid-s750" xml:space="preserve">latitu <lb/>dinem verò mucronis anguli qui fiet, volo eſſe trium <lb/>vel quatuor pedum, redeundo ad feneſtræ corpus, vt <lb/>meliùs declarabitur ad calcem decimæ ſequentis figu-<lb/>ræ. </s> <s xml:id="echoid-s751" xml:space="preserve">Sicq́; </s> <s xml:id="echoid-s752" xml:space="preserve">habebimus pro propugnaculi latere pedes <lb/>50: </s> <s xml:id="echoid-s753" xml:space="preserve">pedes ſcilicet 3 pro interuallo quod intercedit <lb/>inter primam feneſtram & </s> <s xml:id="echoid-s754" xml:space="preserve">lateris angulum: </s> <s xml:id="echoid-s755" xml:space="preserve">pedes no-<lb/>uem pro latitudine ipſius primæ feneſtræ extroſum: <lb/></s> <s xml:id="echoid-s756" xml:space="preserve">pedes 30 pro latitudine primæ, quæ vtramq; </s> <s xml:id="echoid-s757" xml:space="preserve">fene-<lb/>ſtram diſcriminat: </s> <s xml:id="echoid-s758" xml:space="preserve">& </s> <s xml:id="echoid-s759" xml:space="preserve">pedes 8 pro latitudine ſecundæ <lb/>feneſtræ: </s> <s xml:id="echoid-s760" xml:space="preserve">qui quidem omnes pedes ſimul juncti 50 <lb/>efficiunt, paſſus ſcilicet decem pro latere. </s> <s xml:id="echoid-s761" xml:space="preserve">Sicq́; </s> <s xml:id="echoid-s762" xml:space="preserve">re-<lb/>manebunt paſſus 12 pro humero, quum ſuprà dede-<lb/>rimus paſſus 22 pro latere & </s> <s xml:id="echoid-s763" xml:space="preserve">humero propu-<lb/>gnaculi. </s> <s xml:id="echoid-s764" xml:space="preserve">Hæc autem omnia manifeſtè <lb/>apparebunt in præſenti decima fi-<lb/>gura, necnon & </s> <s xml:id="echoid-s765" xml:space="preserve">in an-<lb/>tecedenti.</s> <s xml:id="echoid-s766" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div34" type="section" level="1" n="30"> <head xml:id="echoid-head35" xml:space="preserve">DECIMA FIGVRA EST</head> <head xml:id="echoid-head36" style="it" xml:space="preserve">hîc inſerenda.</head> <pb o="70" file="0070" n="88" rhead=""/> <p> <s xml:id="echoid-s767" xml:space="preserve">Volentes exſtruere gradus ſiue ſcalas feneſtrarum <lb/>tormentariarum à parte extrinſeca in latus, metiemur <lb/>pedes quinque introuerſus, ad lineam quæ terminat <lb/>latitudinem feneſtræ tormentariæ ad ipſum latus ſeu <lb/>cortinam: </s> <s xml:id="echoid-s768" xml:space="preserve">& </s> <s xml:id="echoid-s769" xml:space="preserve">à puncto ſignato ducetur linea lateri <lb/>parallela, tribus pedibus diſtans ab vtraque feneſtra. <lb/></s> <s xml:id="echoid-s770" xml:space="preserve">Deinde, ab ipſo puncto ſignato ad extremitatem ex-<lb/>trinſecam dictæ feneſtræ verſus ipſum latus ducetur <lb/>alia linea: </s> <s xml:id="echoid-s771" xml:space="preserve">ſicq́; </s> <s xml:id="echoid-s772" xml:space="preserve">formati erunt gradus dictæ feneſtræ, <lb/>vt ex noſtris deſcriptionibus patet.</s> <s xml:id="echoid-s773" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s774" xml:space="preserve">Figura ſuprà proximè depicta, quæ integram exſtru-<lb/>ctionem partis vnius fabricæ oſtendit, ad id efficta eſt, <lb/>vt per lineas oſtendat quid expectandum ſit à bom-<lb/>bardis feneſtrarum tormentariarum, & </s> <s xml:id="echoid-s775" xml:space="preserve">vt hinc di-<lb/>gnoſcatur quàm conſideratè deſignari debeant eæ fe-<lb/>neſtræ, reliquaq́; </s> <s xml:id="echoid-s776" xml:space="preserve">omnia quæ ad eas neceſſariò ſpectãt.</s> <s xml:id="echoid-s777" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s778" xml:space="preserve">Iam ſtatuentes extruere feneſtras plateæ inferioris, <lb/>necnon & </s> <s xml:id="echoid-s779" xml:space="preserve">latitudines earum extrinſecas & </s> <s xml:id="echoid-s780" xml:space="preserve">intrinſecas, <lb/>ita vt bombardarum effectus bene cedant, ac ſecun-<lb/>dùm id quod fieri debet, ſtatuemus ſpiſſitudinem <lb/>lateris ad altitudinem vſque, pedum eſſe quindecim, <lb/>(ejuſdem etiam altitudinis ſtatuuntur eſſe primæ fe-<lb/>neſtræ tormentariæ à parte extrinſeca planitiei foſſæ) <lb/>& </s> <s xml:id="echoid-s781" xml:space="preserve">ſecundùm hanc altitudinem ſpiſſitudo lateris tribus <lb/>minuetur pedibus, quum ſingulis quinis pedibus v-<lb/>nus pes inclinationis attribuatur, vt ſuprà dictum eſt. <lb/></s> <s xml:id="echoid-s782" xml:space="preserve">Si itaq; </s> <s xml:id="echoid-s783" xml:space="preserve">ſtatuatur latus in fundamento ſpiſſum eſſe, <lb/>abſque ſcamno (banqucttc ou zcſai@) fundamenti, pe-<lb/>des 35, erit ſpiſſitudo ipſius lateris ad primas feneſtras <lb/>pedes 34. </s> <s xml:id="echoid-s784" xml:space="preserve">Diſtantia verò à primis vnius propugnacu-<lb/>li feneſtris, ad primas alterius, eſt 151 paſſuum cum <pb o="71" file="0071" n="89" rhead=""/> vno pede, quia ſuprà ſtatuimus propugnaculum à pro <lb/>pugnaculo abeſſe paſſus 150. </s> <s xml:id="echoid-s785" xml:space="preserve">Hæc autem diſtantia <lb/>ſupputatur à fundamento vnius ad fundamentum al-<lb/>terius, nulla tamen habita ratione ipſius ſcamni. </s> <s xml:id="echoid-s786" xml:space="preserve">Su-<lb/>pradictis conſideratis ſtatuetur deſignatum punctum <lb/>c, diſtans à linea quæ cortinam format tribus pedibus, <lb/>ita vt bombardæ primæ feneſtræ tormentariæ poſſint <lb/>ipſam euerrere cortinam, ſi ad eam applicatæ eſſent <lb/>ab hoſtibus ſcalæ. </s> <s xml:id="echoid-s787" xml:space="preserve">Statuamus autem hoc punctum c <lb/>ſignatum eſſe introrſum paſſus 5 cum 4 pedibus, ita <lb/>vt deſint ei tantùm tres pedes ad ſupplendam lateris <lb/>ſpiſſitudinem, qualem ſtatuimus latam eſſe introrſum <lb/>feneſtram tormentariam, & </s> <s xml:id="echoid-s788" xml:space="preserve">vt apparet in infraſcripta <lb/>figura. </s> <s xml:id="echoid-s789" xml:space="preserve">A puncto c ad lineam <emph style="sc">AB</emph> ducemus lineam pa-<lb/>rallelam ſeu æquidiſtantem, quæ erit linea CD.</s> <s xml:id="echoid-s790" xml:space="preserve"> Et <lb/>denuò ab eodem puncto <emph style="sc">c</emph> ducetur alia linea æquidi-<lb/>ſtans lineæ <emph style="sc">AP</emph>, quæ præſeferet lateris latitudinem cum <lb/>humero propugnaculi, eritq́; </s> <s xml:id="echoid-s791" xml:space="preserve">linea <emph style="sc">QR</emph>: </s> <s xml:id="echoid-s792" xml:space="preserve">ducentur au-<lb/>tem hæ lineæ per quartam operationem, vt ex noſtra <lb/>deſcriptione colligi poteſt. </s> <s xml:id="echoid-s793" xml:space="preserve">A puncto <emph style="sc">D</emph> verò duce-<lb/>tur perpendicularis infinita, quæ propugnaculi fron-<lb/>tem ſecabit in puncto <emph style="sc">L</emph>: </s> <s xml:id="echoid-s794" xml:space="preserve">fietq́; </s> <s xml:id="echoid-s795" xml:space="preserve">hoc per ſecundam o-<lb/>perationem: </s> <s xml:id="echoid-s796" xml:space="preserve">produceturq́; </s> <s xml:id="echoid-s797" xml:space="preserve">linea <emph style="sc">DL</emph> aduſque punctum <lb/><emph style="sc">F</emph>, pro foſſæ latitudine, vbi bombardæ primæ feneſtræ <lb/>debeunt euerrere murum extrinſecum, (Galli con-<lb/>trcſcazpc.) </s> <s xml:id="echoid-s798" xml:space="preserve">Latitudo autem ipſius foſſæ minor eſſe non <lb/>debet, quàm ſunt latus & </s> <s xml:id="echoid-s799" xml:space="preserve">humerus propugnaculi. </s> <s xml:id="echoid-s800" xml:space="preserve">Iam, <lb/>ad inueſtigandam latitudinem extrinſecam primæ fe-<lb/>neſtræ, dicemus, Si linea <emph style="sc">CD</emph>, quæ eſt paſſuum 182 <lb/>cum duobus pedibus, mihi dat lineam <emph style="sc">DF</emph>, quæ eſt <lb/>paſſuum 47, quid mihi dabit linea <emph style="sc">QA</emph>, quæ eſt paſ- <pb o="72" file="0072" n="90" rhead=""/> ſuum 5 cum 4 pedibus. </s> <s xml:id="echoid-s801" xml:space="preserve">Multiplicando paſſus 47, <lb/>cum paſſibus 5 & </s> <s xml:id="echoid-s802" xml:space="preserve">pedibus 4, prodibunt paſſus 272 & </s> <s xml:id="echoid-s803" xml:space="preserve"><lb/>pedes 3: </s> <s xml:id="echoid-s804" xml:space="preserve">hos autem paſſus 272 pedes 3 diuidemus per <lb/>paſſus 182 & </s> <s xml:id="echoid-s805" xml:space="preserve">pedes 2, prodibunt pedes 7 cum dimi-<lb/>dio pro latitudine extrinſeca primæ feneſtræ tormen-<lb/>tariæ: </s> <s xml:id="echoid-s806" xml:space="preserve">& </s> <s xml:id="echoid-s807" xml:space="preserve">ad hos 7 pedes cum dimidio addemus pe-<lb/>dem vnum pro parte ipſius latitudinis, ad liberiorem <lb/>bombardæ deambulationem: </s> <s xml:id="echoid-s808" xml:space="preserve">itaq́; </s> <s xml:id="echoid-s809" xml:space="preserve">fient pedes 8 cum <lb/>dimidio, tantaq́; </s> <s xml:id="echoid-s810" xml:space="preserve">erit latitudo extrinſeca primæ fene-<lb/>ſtræ tormentariæ. </s> <s xml:id="echoid-s811" xml:space="preserve">Ad habendam autem latitudinem <lb/>ſecundæ feneſtræ, primò ſumetur latitudo primæ, <lb/>ſemipede addito pro libera deambulatione bombar-<lb/>dæ: </s> <s xml:id="echoid-s812" xml:space="preserve">ſtatuamus autem illam eſſe paſſuum 6: </s> <s xml:id="echoid-s813" xml:space="preserve">auferemus <lb/>à linea <emph style="sc">AP</emph>, initium ſumentes à linea <emph style="sc">CD</emph>, paſſus 6, ad-<lb/>uſque punctum <emph style="sc">N</emph>, & </s> <s xml:id="echoid-s814" xml:space="preserve">à puncto <emph style="sc">N</emph> ducemus lineam æ-<lb/>quidiſtantem lineæ <emph style="sc">CD</emph>, quæ erit linea <emph style="sc">NO</emph>: </s> <s xml:id="echoid-s815" xml:space="preserve">deinde di-<lb/>cemus, Si paſſus 75 cum tribus pedibus, <emph style="sc">AI</emph> ſcilicet <lb/>cortinæ dimidium, mihi dant lineam <emph style="sc">AN</emph>, tribus pedi-<lb/>bus exceptis, quæ ſic erit paſſuum 6, quid mihi dabit <lb/>linea <emph style="sc">NO</emph>, quæ eſt paſſuum 5 cum pedibus 4? </s> <s xml:id="echoid-s816" xml:space="preserve">Si multi-<lb/>plices paſſus 5, & </s> <s xml:id="echoid-s817" xml:space="preserve">pedes 4, cum paſſibus 6, prodibunt <lb/>paſſus 34 cum pedibus 4, diuidendi per paſſus 75 cum <lb/>3 pedibus. </s> <s xml:id="echoid-s818" xml:space="preserve">At paſſus 34 cum pedibus 4 diuidi non <lb/>poſſunt per paſſus 75 cum 3 pedibus: </s> <s xml:id="echoid-s819" xml:space="preserve">paſſus igitur il-<lb/>los 34 cum 4 pedibus in pedes reducemus, multipli-<lb/>cando vnumquemque paſſum per 5, prodibunt 174, <lb/>quos diuidemus per paſſus 75 cum 3 pedibus, prodi-<lb/>bunt duo pedes, ac paulo plus: </s> <s xml:id="echoid-s820" xml:space="preserve">tantaq́; </s> <s xml:id="echoid-s821" xml:space="preserve">erit linea <emph style="sc">OG</emph>. <lb/></s> <s xml:id="echoid-s822" xml:space="preserve">Iam à puncto <emph style="sc">G</emph> ducam lineam æquidiſtantem lineæ <lb/><emph style="sc">CD</emph>, quæ erit linea <emph style="sc">GH</emph> infinita. </s> <s xml:id="echoid-s823" xml:space="preserve">A puncto autem <emph style="sc">F</emph> an-<lb/>guli propugnaculi ducemus lineam perpendicularem <pb o="73" file="0073" n="91" rhead=""/> in lineam <emph style="sc">GH</emph>, quæ cadet in punctum <emph style="sc">H</emph>. </s> <s xml:id="echoid-s824" xml:space="preserve">Producemus <lb/>deinde lineam <emph style="sc">HK</emph> aduſque punctum <emph style="sc">M</emph> per foſſæ me-<lb/>dium: </s> <s xml:id="echoid-s825" xml:space="preserve">& </s> <s xml:id="echoid-s826" xml:space="preserve">hoc, quantum quantum eſt, eſt id quod vo-<lb/>lumus bombardas ſecundæ feneſtræ euerrere, foſſu-<lb/>lam ſcilicet, quam ſtatuimus eſſe in medio magnæ foſ-<lb/>ſæ, ſi tamen aqua in foſſa exiſteret. </s> <s xml:id="echoid-s827" xml:space="preserve">At ſi fortè nulla in-<lb/>eſſet foſſæ aqua, ſatis eſſet, ſi bombardæ ſecundæ fene-<lb/>ſtræ euerrerent propugnaculi angulum cum omni eo <lb/>quod introrſum eſt, donec ad minimum rectà ferirent <lb/>collimando aduſque medium cortinæ, quæ eſt inter <lb/>vnum & </s> <s xml:id="echoid-s828" xml:space="preserve">alterum propugnaculum, vt dictum eſt. </s> <s xml:id="echoid-s829" xml:space="preserve">Ve-<lb/>rùm, ad ea quæ ſuprà dicere cœperamus redeuntes, di-<lb/>cemus, Si linea <emph style="sc">GH</emph>, quæ eſt paſſuum 203 cum tribus <lb/>pedibus, dat mihi lineam <emph style="sc">KM</emph>, quæ eſt paſſuum 31, quid <lb/>mihi dabit linea <emph style="sc">MO</emph>, quæ eſt paſſuum 5 cum 4 pedi-<lb/>bus? </s> <s xml:id="echoid-s830" xml:space="preserve">Multiplicabimus paſſus 31 cum paſſibus 5 & </s> <s xml:id="echoid-s831" xml:space="preserve">pe-<lb/>dibus 4, prodibunt paſſus 198 & </s> <s xml:id="echoid-s832" xml:space="preserve">pedes duo, quos di-<lb/>uidemus per paſſus 203 & </s> <s xml:id="echoid-s833" xml:space="preserve">pedes 3, prodibunt ferſe4; </s> <s xml:id="echoid-s834" xml:space="preserve">4 <lb/>pedes cum dimidio, quibus addemus pedes duos cum <lb/>dimidio, quos ſuprà habebamus, prodibunt ſeptem <lb/>pedes, quibus ſemipedem addemus, pro altera parte <lb/>extrinſecæ latitudinis feneſtræ, idq́; </s> <s xml:id="echoid-s835" xml:space="preserve">ad liberiorem red-<lb/>dendam bombardæ deambulationem, (vt & </s> <s xml:id="echoid-s836" xml:space="preserve">in prima <lb/>feneſtra tormentaria factum eſt.) </s> <s xml:id="echoid-s837" xml:space="preserve">Hæc ſimul juncta, fa-<lb/>cient pedes ſeptem cum dimidio: </s> <s xml:id="echoid-s838" xml:space="preserve">ac tanta erit latitu-<lb/>do extrinſeca ſecundæ feneſtræ, ſcilicet <emph style="sc">NS</emph>.</s> <s xml:id="echoid-s839" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s840" xml:space="preserve">Habitis latitudinibus extrinſecis feneſtrarum tor-<lb/>mentariarum, jam oſtendemus modum adipiſcendi <lb/>latitudines intrinſecas, necnon & </s> <s xml:id="echoid-s841" xml:space="preserve">latitudines duorum <lb/>punctorum <emph style="sc">C</emph> & </s> <s xml:id="echoid-s842" xml:space="preserve"><emph style="sc">G</emph>. </s> <s xml:id="echoid-s843" xml:space="preserve">Ad id aſſequendum, apponetur <lb/>regula ad extremitatem latitudinum extrinſecarum <pb o="74" file="0074" n="92" rhead=""/> feneſtrarum tormentariarum, & </s> <s xml:id="echoid-s844" xml:space="preserve">ad duo puncta, <emph style="sc">C</emph> & </s> <s xml:id="echoid-s845" xml:space="preserve"><emph style="sc">G</emph>, <lb/>producendo à parte interiori lineas in infinitum. </s> <s xml:id="echoid-s846" xml:space="preserve">Præ-<lb/>terea, à parte intrinſeca ad extremitates craſſitiei ſeu <lb/>ſpiſſitudinis lateris, dimetientur pedes quinque, & </s> <s xml:id="echoid-s847" xml:space="preserve">ad <lb/>puncta <emph style="sc">C</emph> & </s> <s xml:id="echoid-s848" xml:space="preserve"><emph style="sc">G</emph> pedes 3, relinquentes nihilominus in <lb/>medio lineas productas & </s> <s xml:id="echoid-s849" xml:space="preserve">puncta <emph style="sc">C</emph> & </s> <s xml:id="echoid-s850" xml:space="preserve"><emph style="sc">G</emph>, vt videre eſt <lb/>in figura. </s> <s xml:id="echoid-s851" xml:space="preserve">Habita latitudine tum extrinſeca tum intrin-<lb/>ſeca, necnon & </s> <s xml:id="echoid-s852" xml:space="preserve">latitudine duorum punctorum <emph style="sc">C</emph> & </s> <s xml:id="echoid-s853" xml:space="preserve"><emph style="sc">G</emph> <lb/>feneſtrarum tormentariarum, habebitur longitudo & </s> <s xml:id="echoid-s854" xml:space="preserve"><lb/>latitudo platearum inferiorum hunc in modum: </s> <s xml:id="echoid-s855" xml:space="preserve">In <lb/>extremitatibus latitudinum feneſtrarum tormentaria-<lb/>rum à parte intrinſeca, metientur ab vtraque parte di-<lb/>ctarum feneſtrarum pedes 5: </s> <s xml:id="echoid-s856" xml:space="preserve">& </s> <s xml:id="echoid-s857" xml:space="preserve">ab his quinque pedi-<lb/>bus ſignatis ducentur lineæ æquidiſtãtes iis quæ à par-<lb/>te intrinſeca productæ ſunt, quæq́; </s> <s xml:id="echoid-s858" xml:space="preserve">finiunt latitudines <lb/>feneſtrarum extrinſecus. </s> <s xml:id="echoid-s859" xml:space="preserve">Harum duarum linearum æ-<lb/>quidiſtanter ductarum ad lineas primæ feneſtræ, altera <lb/>inſeruit pro termino pilæ lapideæ, altera pro termino <lb/>alæ propugnaculi: </s> <s xml:id="echoid-s860" xml:space="preserve">duarum autem linearum, quæ à <lb/>duobus punctis ſignatis in ſecunda feneſtra ducuntur, <lb/>æquidiſtantes ſuis lineis productis, altera parallela eſt <lb/>fronti propugnaculi, altera terminat aliam pilæ lapi-<lb/>deæ partem. </s> <s xml:id="echoid-s861" xml:space="preserve">Hoc facto lineam ducemus lateri paralle-<lb/>lam, pro longitudine plateæ inferioris. </s> <s xml:id="echoid-s862" xml:space="preserve">Atque hoc mo-<lb/>do ſuprà ſcripto, conſtruuntur primæ propugnaculi <lb/>plateæ, cum aliis rebus neceſſariis, vt ſuprà dictum eſt <lb/>in figuris ſeptima & </s> <s xml:id="echoid-s863" xml:space="preserve">octaua, ac vt etiam ex hac vnde-<lb/>cima dignoſci poteſt.</s> <s xml:id="echoid-s864" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div35" type="section" level="1" n="31"> <head xml:id="echoid-head37" xml:space="preserve">VNDECIMA FIGVRA AD</head> <head xml:id="echoid-head38" xml:space="preserve">_hanc paginam ſpectat._</head> <pb file="0075" n="93"/> <pb o="76" file="0076" n="94" rhead=""/> <p> <s xml:id="echoid-s865" xml:space="preserve">Deſignata latitudine feneſtrarum tormentariarum, <lb/>aliisq́; </s> <s xml:id="echoid-s866" xml:space="preserve">rebus neceſſariis quæ ad primam plateam perti-<lb/>nent, continuabimus fabricam noſtram ad ſecundam <lb/>plateam vſque, relinquentes muro à parte extrinſeca <lb/>in ſingulos quinque pedes pedem vnum inclinationis, <lb/>vt ſuprà dictum eſt: </s> <s xml:id="echoid-s867" xml:space="preserve">qui quidem murus à parte interio-<lb/>ri æquidiſtans fiet ſuperficiei exteriori. </s> <s xml:id="echoid-s868" xml:space="preserve">Volo itidem vt <lb/>caput anteridum, quod ipſi muro annectitur, æqui-<lb/>diſtans ſit parti exteriori muri:</s> <s xml:id="echoid-s869" xml:space="preserve">alterum verò caput ma-<lb/>gis interius volo ad perpendiculum ædificari. </s> <s xml:id="echoid-s870" xml:space="preserve">Aduer-<lb/>tendum eſt etiam, vt fabricando parietem extrinſecum <lb/>(Gal. </s> <s xml:id="echoid-s871" xml:space="preserve">contrcſcazpc,) cum ſua via operta, paries ille fiat de-<lb/>miſſus quantum fieri poſſit, ne hoſtes eo vtantur pro <lb/>lorica. </s> <s xml:id="echoid-s872" xml:space="preserve">Vellem etiam vt is paries extrinſecus exſtructus <lb/>eſſet cum ſuis anteridibus, aduſque viam opertam. </s> <s xml:id="echoid-s873" xml:space="preserve">Pin-<lb/>na, quæ vtramq; </s> <s xml:id="echoid-s874" xml:space="preserve">feneſtram tormentariam interjacet, <lb/>initium ſumens à platea inferiori, fabricatur ex muro <lb/>ſolido, vel cum anteridibus: </s> <s xml:id="echoid-s875" xml:space="preserve">inter quarum capita, à <lb/>parte interiori fit murus ſpiſſitudine trium aut quin-<lb/>que pedum: </s> <s xml:id="echoid-s876" xml:space="preserve">deinde quod vacuum eſt inter anteridem <lb/>& </s> <s xml:id="echoid-s877" xml:space="preserve">anteridem, repletur optima terra, quæ impensè cal-<lb/>catur. </s> <s xml:id="echoid-s878" xml:space="preserve">Pinnam autem hanc nollem vlteriùs aſſurgere <lb/>quàm par eſt, ne bombardæ plateæ ſuperioris ab ea <lb/>impediantur: </s> <s xml:id="echoid-s879" xml:space="preserve">cupio enim eas ad medium vſque foſſæ <lb/>ferire rectà collimando. </s> <s xml:id="echoid-s880" xml:space="preserve">Omnes anterides & </s> <s xml:id="echoid-s881" xml:space="preserve">pilæ la-<lb/>pideæ, quæ ſuper primis plateis deſignatæ ſunt, aſſur-<lb/>gunt in altitudinem à 12 in 15 pedes: </s> <s xml:id="echoid-s882" xml:space="preserve">dehinc fornices <lb/>exſtruuntur, ad fulciendas ſecundas plateas. </s> <s xml:id="echoid-s883" xml:space="preserve">Spiſſitu-<lb/>dines murorum, quæ fiunt ac deſignantur circum pla-<lb/>teas inferiores, exſurgunt in eam altitudinem in quam <lb/>& </s> <s xml:id="echoid-s884" xml:space="preserve">anterides, vt ſuper ipſis fornices exſtruantur. </s> <s xml:id="echoid-s885" xml:space="preserve">Muri <pb o="77" file="0077" n="95" rhead=""/> autem iſti impediunt ac vetant ne terra in ipſam pla-<lb/>team cadat. </s> <s xml:id="echoid-s886" xml:space="preserve">Illic etiam formantur muri viarum, quæ <lb/>ad inferiores plateas tendunt, necnon & </s> <s xml:id="echoid-s887" xml:space="preserve">ij qui vtram-<lb/>que plateam interjacent, ſpiſſitudine quatuor aut quin <lb/>que pedum. </s> <s xml:id="echoid-s888" xml:space="preserve">Fabricantur etiam cortinæ cum ſuis an-<lb/>teridibus, & </s> <s xml:id="echoid-s889" xml:space="preserve">alia ad deſignationem propugnaculorum <lb/>neceſſaria, vnumquodque cum ſuis legitimis menſu-<lb/>ris. </s> <s xml:id="echoid-s890" xml:space="preserve">Vt autem pleriſque omnibus morem gereremus, <lb/>anterides ita formauimus, vt ſtrictiores eſſent arcem <lb/>verſus, ſpiſſiores verò vbi muro annectuntur, vt mani-<lb/>feſtè apparet in media parte iſtius propugnaculi, in <lb/>duodecima ſcilicet figura, in parte ſignata <emph style="sc">B</emph>. </s> <s xml:id="echoid-s891" xml:space="preserve">Supradi-<lb/>ctis ad exitum perductis, dabitur opera, vt arcus ex-<lb/>ſtruantur ad fornices faciendos ab vna anteride ad al-<lb/>teram in fronte & </s> <s xml:id="echoid-s892" xml:space="preserve">humero propugnaculi, necnon & </s> <s xml:id="echoid-s893" xml:space="preserve"><lb/>in cortina. </s> <s xml:id="echoid-s894" xml:space="preserve">Exſtruentur etiam frontes viarum quæ ad <lb/>plateas tendunt, iiq́; </s> <s xml:id="echoid-s895" xml:space="preserve">qui ab vna platea ad aliam. </s> <s xml:id="echoid-s896" xml:space="preserve">Su-<lb/>perior pars horum fornicum benè adæquabitur, vt <lb/>poſtea incipiamus loricam exſtruere. </s> <s xml:id="echoid-s897" xml:space="preserve">Et hæc <lb/>omnia manifeſtè in figura duode-<lb/>cima apparent, in parte <lb/>A ſignata.</s> <s xml:id="echoid-s898" xml:space="preserve"/> </p> <pb o="78" file="0078" n="96" rhead=""/> <figure> <image file="0078-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0078-01"/> <caption xml:id="echoid-caption8" xml:space="preserve">DVODECIMA<gap/>FIGVRA.</caption> </figure> <pb file="0078_0079" n="97"/> <pb o="79" file="0079" n="98" rhead=""/> <figure> <image file="0079-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0079-01"/> </figure> <pb o="80" file="0080" n="99" rhead=""/> <p> <s xml:id="echoid-s899" xml:space="preserve">Sit jam nobis lorica propugnaculi exſtruẽda. </s> <s xml:id="echoid-s900" xml:space="preserve">Dabi-<lb/>mus ei pedes octo vel nouem altitudinis à cingulo ad <lb/>ſummitatem ipſius. </s> <s xml:id="echoid-s901" xml:space="preserve">Loricam verò cortinæ altam fa-<lb/>ciemus pedum ſex vel ſeptem. </s> <s xml:id="echoid-s902" xml:space="preserve">Has autem loricas qui-<lb/>dam vellent intrò trahi duobus aut tribus pedibus, à <lb/>cingulo in ſuprà, vt iis oppugnatis rudera remanerent <lb/>intra arcem, nec pro ſcala hoſti eſſent. </s> <s xml:id="echoid-s903" xml:space="preserve">Hæ autem lo-<lb/>ricæ altiores fiunt in vno loco quàm in alio: </s> <s xml:id="echoid-s904" xml:space="preserve">altiores <lb/>enim debent eſſe loricæ propugnaculi quàm cortinæ, <lb/>vt ipſa propugnacula poſſint è parte ſuperiori ſeſe in-<lb/>uicem euerrere, necnon & </s> <s xml:id="echoid-s905" xml:space="preserve">loricam cortinæ, cum o-<lb/>mni aggere terreo, (tczbcpſciy.) </s> <s xml:id="echoid-s906" xml:space="preserve">Loricam propugna-<lb/>culi & </s> <s xml:id="echoid-s907" xml:space="preserve">cortinæ nollem eſſe in ſpiſſitudine minorem vi <lb/>ginti vel vigintiquatuor pedibus. </s> <s xml:id="echoid-s908" xml:space="preserve">Ad exſtruendam <lb/>igitur eam loricam à cingulo in ſuprà, duos muros ex-<lb/>ſtruemus, duos aut tres pedes ſpiſſos, ita vt alter alte-<lb/>rum non excedat in ſpiſſitudine: </s> <s xml:id="echoid-s909" xml:space="preserve">diſtabunt autem hi <lb/>muri alter ab altero interuallo ſpiſſitudinis loricæ. </s> <s xml:id="echoid-s910" xml:space="preserve">Mu-<lb/>rum foſſæ propiorem volo exſtrui cum inclinatione, <lb/>ſingulis octo pedibus vnum inclinationis tribuendo. <lb/></s> <s xml:id="echoid-s911" xml:space="preserve">Volo tamen vt pars interior ipſius muri æquidiſtet par <lb/>ti extrinſecæ. </s> <s xml:id="echoid-s912" xml:space="preserve">Alterum autem murum, qui magis in-<lb/>terior, volo erigi ad perpendiculum ab vtraque parte. </s> <s xml:id="echoid-s913" xml:space="preserve"><lb/>Interuallum inter hos duos muros, optima terra im-<lb/>pleatur, quæ impensè calcetur ac prematur. </s> <s xml:id="echoid-s914" xml:space="preserve">Intra hoſ-<lb/>ce duos muros, vellem poſt ſingulos denos aut duo-<lb/>denos pedes murum ſolidum exſtrui, duos aut tres pe-<lb/>des ſpiſſum, qui hoſce duos muros inſimul ligaret, & </s> <s xml:id="echoid-s915" xml:space="preserve"><lb/>veluti concatenaret. </s> <s xml:id="echoid-s916" xml:space="preserve">Superficiem autem ſupremam <lb/>loricæ, tum propugnaculi, tum cortinæ, inclinatam vel-<lb/>lem eſſe foſſam verſus, vt qui ad eam loricam ſtant, poſ- <pb o="81" file="0081" n="100" rhead=""/> ſint parietem extrinſecum inſpicere, aduſque mediam <lb/>ipſius partem & </s> <s xml:id="echoid-s917" xml:space="preserve">vltra. </s> <s xml:id="echoid-s918" xml:space="preserve">Hanc autem ſuperficiem vellem <lb/>operiri optimo ſaxo, tenui quidem, ſed valdè lato, & </s> <s xml:id="echoid-s919" xml:space="preserve"><lb/>polito, vel alia materia quãtum fieri poterit ſolida, tum <lb/>ne hoſtes in murum aſcendentes locum reperiant, in <lb/>quem poſſint manus infigere vel inſerere, tum etiam <lb/>vt imbrium tempore aqua pluuia in foſſam de-<lb/>labatur. </s> <s xml:id="echoid-s920" xml:space="preserve">Hæc autem omnia manifeſtiùs <lb/>apparent in decimatertia figu-<lb/>ra, in parte ſignata A.</s> <s xml:id="echoid-s921" xml:space="preserve"/> </p> <figure> <image file="0081-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0081-01"/> </figure> <figure> <image file="0081-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0081-02"/> </figure> <pb o="82" file="0082" n="101" rhead=""/> <figure> <image file="0082-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0082-01"/> <caption xml:id="echoid-caption9" xml:space="preserve">DECIMATIA FIGVRA.</caption> </figure> <pb file="0082_0083" n="102"/> <pb o="83" file="0083" n="103" rhead=""/> <figure> <image file="0083-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0083-01"/> </figure> <pb o="84" file="0084" n="104" rhead=""/> <p> <s xml:id="echoid-s922" xml:space="preserve">Alicubi, ad loricam tum propugnaculi, tum cor-<lb/>tinæ, vellem eſſe ſcamnum cum ſuis gradibus, alicubi <lb/>verò non. </s> <s xml:id="echoid-s923" xml:space="preserve">Vbi terra extrinſecus alta eſt, tunc vellem <lb/>aptari ſcamnum cum ſuis gradibus: </s> <s xml:id="echoid-s924" xml:space="preserve">vbi verò depreſſa <lb/>eſt terra, tunc nec ſcamnum vellem, nec gradus, ſed <lb/>tantùm vt eſſent operti milites qui ad loricam. </s> <s xml:id="echoid-s925" xml:space="preserve">Sca-<lb/>mnum propugnaculi nollem eſſe in latitudine minus <lb/>tribus aut quatuor pedibus. </s> <s xml:id="echoid-s926" xml:space="preserve">Altitudo loricæ, tum <lb/>propugnaculi, tum cortinæ, non debet aſſurgere vl-<lb/>tra quatuor pedes, aut quatuor cum dimidio ſupra <lb/>ſcamnum. </s> <s xml:id="echoid-s927" xml:space="preserve">Gradus, qui ad ſcamnum propugnaculi, mi-<lb/>nores eſſe non debent duobus pedibus, vel duobus <lb/>cum dimidio. </s> <s xml:id="echoid-s928" xml:space="preserve">Aggerem terreum, qui ad loricam, nol-<lb/>lem eſſe minorem in latitudine ab ipſa lorica decem <lb/>paſſibus. </s> <s xml:id="echoid-s929" xml:space="preserve">Aſcenſus, ſiue inclinatio, qua ſupra aggerem <lb/>aſcenditur, nollem eſſe minorem paſſibus quinque: <lb/></s> <s xml:id="echoid-s930" xml:space="preserve">huncq́; </s> <s xml:id="echoid-s931" xml:space="preserve">aſcenſum vellem liberum relinqui, abſque vllo <lb/>impedimento, vt vndecumque poſſent milites aſcen-<lb/>dere. </s> <s xml:id="echoid-s932" xml:space="preserve">Conclauia arcis vellem ad minus abeſſe ab ag-<lb/>geris aſcenſu ſeptem aut octo paſſus, vt faciliùs poſſint <lb/>fieri receſſus, (Galli dicunt rctzaictcs, rctranchcmcnts) <lb/>ſi oppugnatio & </s> <s xml:id="echoid-s933" xml:space="preserve">cuniculi hoſtiles ad id nos adigant. </s> <s xml:id="echoid-s934" xml:space="preserve"><lb/>In via operta fit etiam ab ea aſcenſus inclinatus, vt fit <lb/>in aggere intrinſeco, idq́; </s> <s xml:id="echoid-s935" xml:space="preserve">ad faciliùs ſaliendum in ag-<lb/>gerem extrinſecum: </s> <s xml:id="echoid-s936" xml:space="preserve">attamen potiùs probarem, vt fie-<lb/>rent vnus & </s> <s xml:id="echoid-s937" xml:space="preserve">alter gradus, cum ſuo ſcamno bene adæ-<lb/>quato pedem cum dimidio lato, vel circum, cum ſua <lb/>lorica ad perpendiculum, vt milites, qui ad eam, con-<lb/>ſpicui tantùm eſſent à pectore in ſuprà, vel tantum <lb/>quantum illis eſſet commodum ad aptanda arma, & </s> <s xml:id="echoid-s938" xml:space="preserve"><lb/>ad repellendos furores hoſtiles. </s> <s xml:id="echoid-s939" xml:space="preserve">Via operta lata ſit à 5 <pb o="85" file="0085" n="105" rhead=""/> in 8 pedes, & </s> <s xml:id="echoid-s940" xml:space="preserve">ita depreſſa ab aggere extrinſeco, vt ij qui <lb/>per eam gradiuntur, ab hoſtibus videri non poſſint, <lb/>quinque ſcilicet aut ſex pedes à ſummitate aggeris ex-<lb/>trinſeci infrà. </s> <s xml:id="echoid-s941" xml:space="preserve">Aduertendum etiam eſt, ne cingulum <lb/>(Galli ceinctuzc, cordoy) tum cortinæ, tum propugnacu-<lb/>li altiùs collocetur, quàm eſt ſuprema inclinatio muri: <lb/></s> <s xml:id="echoid-s942" xml:space="preserve">meliusq́; </s> <s xml:id="echoid-s943" xml:space="preserve">eſſet vt paulo infra eam collocaretur, quàm <lb/>ſuprà. </s> <s xml:id="echoid-s944" xml:space="preserve">Præterea bonum eſſet vt foſſa profundior eſſet <lb/>altitudine ſoli cui ſuperædificantur conclauia arcis in-<lb/>trinſeca, vt immundicies arcis faciliùs poſſent in ipſam <lb/>foſſam delabi, quia ſalubriori aëre fruerentur, qui ar-<lb/>cem inhabitant, & </s> <s xml:id="echoid-s945" xml:space="preserve">arx difficiliùs expugnaretur, foſ-<lb/>ſam adeò profundam habens. </s> <s xml:id="echoid-s946" xml:space="preserve">Neceſſe etiam eſſet, vt <lb/>milites, qui adloricam tum propugnaculi, tum cortinę, <lb/>non ſolùm murum & </s> <s xml:id="echoid-s947" xml:space="preserve">aggerem extrinſecos poſſent in-<lb/>ſpicere, ſed etiam poſſent oculis luſtrare ad ſexcentos <lb/>aut ſeptingentos paſſus planitiei vicinæ, ne inibi vllus <lb/>eſſet, qui è lorica tum propugnaculi, tum cor-<lb/>tinæ, diſcerni non poſſet, vt hîc in <lb/>decimaquarta figura <lb/>apparet.</s> <s xml:id="echoid-s948" xml:space="preserve"/> </p> <figure> <image file="0085-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0085-01"/> </figure> <pb o="86" file="0086" n="106" rhead=""/> <figure> <image file="0086-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0086-01"/> <caption xml:id="echoid-caption10" xml:space="preserve">DECIMAQVA<gap/> FIGVRA.</caption> </figure> <pb file="0086_0087" n="107"/> <pb o="87" file="0087" n="108" rhead=""/> <figure> <image file="0087-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0087-01"/> </figure> <pb o="88" file="0088" n="109" rhead=""/> <p> <s xml:id="echoid-s949" xml:space="preserve">Idem ordo, eædemq́; </s> <s xml:id="echoid-s950" xml:space="preserve">menſuræ obſeruabuntur, vbi <lb/>munitio tantummodo terrea fit, excepto quòd in mu-<lb/>nitionibus terreis plateæ relin quuntur in totum aper-<lb/>tæ, initium ſumendo ab ipſo fundamento adæquato: <lb/></s> <s xml:id="echoid-s951" xml:space="preserve">quæ tamen adæquatio ita fiat, vt, quemadmodum ſu-<lb/>prà dictum eſt, paululum pendeat centrum verſus, re-<lb/>linquendo duos aut tres pedes ſcamni ex fundamen-<lb/>to, vt & </s> <s xml:id="echoid-s952" xml:space="preserve">ſuprà. </s> <s xml:id="echoid-s953" xml:space="preserve">Ad hanc munitionem terra eligenda <lb/>eſt quantum fieri poterit optima. </s> <s xml:id="echoid-s954" xml:space="preserve">Ramuli item ij eligi <lb/>debent, qui rectiores ſunt, nec plus digito craſſiores. </s> <s xml:id="echoid-s955" xml:space="preserve"><lb/>In exſtruendo æquabitur corium vnum ramulorum, <lb/>(architecti Galli dicunt, fairx by ſict dc faſcince,) qui ſum <lb/>mitates ſuas habeant ſibi inuicem oppoſitas, faſciculis <lb/>juxta faſciculos appoſitis, beneq́; </s> <s xml:id="echoid-s956" xml:space="preserve">inſimul alligatis. </s> <s xml:id="echoid-s957" xml:space="preserve">Su-<lb/>per hoc corio aliud ex optima terra apponetur, altum <lb/>ad ſemipedem, impenſeq́; </s> <s xml:id="echoid-s958" xml:space="preserve">calcatum. </s> <s xml:id="echoid-s959" xml:space="preserve">Hocq́; </s> <s xml:id="echoid-s960" xml:space="preserve">ordine ex-<lb/>ſtruetur munitio, vt ſuprà in lapidea fabrica dictum <lb/>eſt. </s> <s xml:id="echoid-s961" xml:space="preserve">Quòd ſi in animo habeamus, hanc terream mu-<lb/>nitionem induſio lapideo, ſeu tunica, ſuperueſtire, (Gal <lb/>li dicunt, chemiſc dc muraiſſe,) anterides etiam huic <lb/>tunicæ adhibebuntur, vt ſuprà factum eſt in munitio-<lb/>ne lapidea.</s> <s xml:id="echoid-s962" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s963" xml:space="preserve">Quum hucuſq; </s> <s xml:id="echoid-s964" xml:space="preserve">dixerimus de fabrica lapidea, nec-<lb/>non & </s> <s xml:id="echoid-s965" xml:space="preserve">de terrea, pretium operæ mihi videtur aliquid <lb/>etiam dicere de planis formis, (Galli dicunt plattcfor-<lb/>mcs,) necnon & </s> <s xml:id="echoid-s966" xml:space="preserve">de vallis prominentibus, (Galli caual-<lb/>ficre.) </s> <s xml:id="echoid-s967" xml:space="preserve">Planæ formæ in medio cortinarum fiunt, cum <lb/>inclinatione in foſſam, eademq́; </s> <s xml:id="echoid-s968" xml:space="preserve">materia qua & </s> <s xml:id="echoid-s969" xml:space="preserve">pro-<lb/>pugnacula. </s> <s xml:id="echoid-s970" xml:space="preserve">Valla prominentia fiunt in medio ipſius <lb/>cortinæ ſupra aggerem terreum, interuallo decem aut <lb/>duodecim pedum à lorica. </s> <s xml:id="echoid-s971" xml:space="preserve">Fiunt etiam in ipſo ore pro- <pb o="89" file="0089" n="110" rhead=""/> pugnaculi. </s> <s xml:id="echoid-s972" xml:space="preserve">Exſtruuntur autem figura quadrangula <lb/>ſeu quadrata, eaq́; </s> <s xml:id="echoid-s973" xml:space="preserve">altitudine, vt bombardæ quæ ſuper <lb/>ipſis deuerrant frontes & </s> <s xml:id="echoid-s974" xml:space="preserve">ſuperiora propugnaculi, & </s> <s xml:id="echoid-s975" xml:space="preserve"><lb/>præterea poſſint in planitiem campeſtrem pilas ſuas <lb/>ejaculari. </s> <s xml:id="echoid-s976" xml:space="preserve">Lorica ipſius valli prominentis ſpiſſa debet <lb/>eſſe à 30 in 40 pedes: </s> <s xml:id="echoid-s977" xml:space="preserve">ejus longitudo à 160 in 170: </s> <s xml:id="echoid-s978" xml:space="preserve">la-<lb/>titudo à 150 in 160 cum ſua inclinatione (eſcharpe.) </s> <s xml:id="echoid-s979" xml:space="preserve">Sic <lb/>autem debet exſtrui vt ſupra eum poſſint imponi ma-<lb/>jores bombardæ. </s> <s xml:id="echoid-s980" xml:space="preserve">Ejus inclinatio debet eſſe dimidia ad <lb/>ipſius altitudinem. </s> <s xml:id="echoid-s981" xml:space="preserve">De vtilitate ac fructu tum plana-<lb/>rum formarum, tum etiam vallorum prominentium, <lb/>tot auctores diſſeruerunt, vt mihi ſuperuacuum viſum <lb/>ſit ampliùs de iis dicere. </s> <s xml:id="echoid-s982" xml:space="preserve">Verùm, vt lectoribus ſatisfiat, <lb/>in decimaquinta figura ſequenti depicta eſt plana for-<lb/>ma inter duo propugnacula, & </s> <s xml:id="echoid-s983" xml:space="preserve">in ore ipſorum propu-<lb/>gnaculorum duo valla prominentia. </s> <s xml:id="echoid-s984" xml:space="preserve">Videri poterit <lb/>etiam vallum prominens in medio cortinæ, vt appa-<lb/>ret in decimaquarta figura.</s> <s xml:id="echoid-s985" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s986" xml:space="preserve">In ſequenti primo propugnaculo ad auriculam <lb/>ſunt feneſtræ tormentariæ primæ plateæ opertæ à duo <lb/>bus fornicibus, qui ſurſum aſcendunt. </s> <s xml:id="echoid-s987" xml:space="preserve">Eſt etiam pila la-<lb/>pidea extrinſecus, figura triangulari, vtramque fene-<lb/>ſtram interjacens. </s> <s xml:id="echoid-s988" xml:space="preserve">Hu jus pilæ baſis eſt ea pars quæ <lb/>vtramq; </s> <s xml:id="echoid-s989" xml:space="preserve">feneſtram inter jacet. </s> <s xml:id="echoid-s990" xml:space="preserve">Eſt autem hæc pila alta <lb/>à foſſæ planitie, ad ſummitatem vſque primarum fe-<lb/>neſtrarum, & </s> <s xml:id="echoid-s991" xml:space="preserve">longa quantum ipſa auricula. </s> <s xml:id="echoid-s992" xml:space="preserve">Ei inniti-<lb/>tur pars duorum fornicum: </s> <s xml:id="echoid-s993" xml:space="preserve">reliquæ partes innituntur, <lb/>altera auriculæ, altera verò cortinæ. </s> <s xml:id="echoid-s994" xml:space="preserve">Supremum ho-<lb/>rum fornicum benè adæquatur, ita tamen vt paululum <lb/>foſſam verſus pendeat. </s> <s xml:id="echoid-s995" xml:space="preserve">Eſt autem hæc procliuitas ea-<lb/>dem cum procliuitate pinnæ ſuperioris, vt ij q́ui <pb o="90" file="0090" n="111" rhead=""/> <pb file="0090_0091" n="112"/> <pb o="91" file="0091" n="113" rhead=""/> <anchor type="figure" xlink:label="fig-0091-01a" xlink:href="fig-0091-01"/> <pb o="92" file="0092" n="114" rhead=""/> ſunt in platea ſuperiori poſſint vltra medium foſſæ in- ſpicere. </s> <s xml:id="echoid-s996" xml:space="preserve">Poſſet etiam accidere, vt ſuper hoc fornice poſſent collocari milites cum bonis ſclopetis ad ipſius foſſæ defenſionem, quia hoſce fornices contegit auri- cula. </s> <s xml:id="echoid-s997" xml:space="preserve">Hoc etiam præſtant hi fornices, ne pilæ ejacula- tæ à bombardis hoſtium (qui ſunt ſuper aggere extrin- ſeco) obturare queant primas feneſtias tormentarias.</s> <s xml:id="echoid-s998" xml:space="preserve"/> </p> <div xml:id="echoid-div35" type="float" level="2" n="1"> <figure xlink:label="fig-0090-01" xlink:href="fig-0090-01a"> <image file="0090-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0090-01"/> </figure> <figure xlink:label="fig-0091-01" xlink:href="fig-0091-01a"> <image file="0091-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0091-01"/> </figure> </div> <p> <s xml:id="echoid-s999" xml:space="preserve"><emph style="sc">Iam</emph> dicemus de introitu ſiue porta, quæ fit vt per <lb/>eam in arcem ingrediamur. </s> <s xml:id="echoid-s1000" xml:space="preserve">Hæc fit in medio cortinæ, <lb/>ſeu juxta vnum propugnaculi latus, cum ſuo ponte li-<lb/>gneo, vt obſidionis tempore poſſit deſtrui vel com-<lb/>buri pons ille. </s> <s xml:id="echoid-s1001" xml:space="preserve">Sit autem hæc porta ita depreſſa, vt ab <lb/>aggere extrinſeco perſpici non poſſit. </s> <s xml:id="echoid-s1002" xml:space="preserve">In introitu ipſius <lb/>portæ vellem eſſe locum aliquem ſaluum: </s> <s xml:id="echoid-s1003" xml:space="preserve">idq́; </s> <s xml:id="echoid-s1004" xml:space="preserve">multis <lb/>de cauſis, ſed præcipuè, vt illic arma militum in tuto <lb/>eſſe poſſent. </s> <s xml:id="echoid-s1005" xml:space="preserve">In pinnæ fundamento, vel juxta propu-<lb/>gnaculi latus fit exitus, quo milites, dum arx oppugna-<lb/>tur, poſſint extra exire, & </s> <s xml:id="echoid-s1006" xml:space="preserve">poſſint etiam tutari foſſam, <lb/>& </s> <s xml:id="echoid-s1007" xml:space="preserve">amouere ruinas ab oppugnatione factas: </s> <s xml:id="echoid-s1008" xml:space="preserve">alioquin <lb/>hæ ruinæ impedimento ſunt feneſtris tormentariis, & </s> <s xml:id="echoid-s1009" xml:space="preserve"><lb/>faciliorem aſcenſum hoſti præbent. </s> <s xml:id="echoid-s1010" xml:space="preserve">Multi vellent cor-<lb/>tinas arcem verſus quaſi plicatas eſſe, cum plana forma <lb/>introrſum vel extrorſum, vel cum vallo prominenti in <lb/>plicatura ſeu angulo ipſius cortinæ. </s> <s xml:id="echoid-s1011" xml:space="preserve">Hi opinionẽ ſuam <lb/>firmant, dicendo, hoſtes ſic magis offendi poſſe, eorũq́; <lb/></s> <s xml:id="echoid-s1012" xml:space="preserve">oppugnationem obliquiorem eſſe: </s> <s xml:id="echoid-s1013" xml:space="preserve">obliqua autem op-<lb/>pugnatio non ita offendit vt recta. </s> <s xml:id="echoid-s1014" xml:space="preserve">At certum eſt, ſi <lb/>hocce modo exſtruerentur cortinæ, non poſſe propu-<lb/>gnaculorum plateas ita amplas eſſe vt ſuprà diximus, <lb/>nec eorum humeri ita firmi vt bombardarum ictus <lb/>pati poſſent. </s> <s xml:id="echoid-s1015" xml:space="preserve">Prætereà hoc modo non facilè fierent <pb o="93" file="0093" n="115" rhead=""/> receſſus, (Galli zctranchements.) </s> <s xml:id="echoid-s1016" xml:space="preserve">Idcirco nollem corti-<lb/>nas eſſe flexas, niſi ſitus lociid à nobis extorqueret: </s> <s xml:id="echoid-s1017" xml:space="preserve">im-<lb/>mo vellem eas directas eſſe ab vno propugnaculo ad <lb/>aliud. </s> <s xml:id="echoid-s1018" xml:space="preserve">Cortinas autem nollem ita longas, vt ſolæ ma-<lb/>jores bombardæ primæ plateæ poſſent euerrere pro-<lb/>pugnaculifrontes, ſed etiam bombardæ minores. </s> <s xml:id="echoid-s1019" xml:space="preserve">Alij <lb/>forſan dicent, cortina breuiori exiſtente, bombardas <lb/>majores offenſuras ipſa arcis propugnacula: </s> <s xml:id="echoid-s1020" xml:space="preserve">huic ob-<lb/>jectioni ita reſpondeo: </s> <s xml:id="echoid-s1021" xml:space="preserve">Vbi hoſtis arcem oppugnat, <lb/>bombardas majores non debere ad defenſionem arcis <lb/>pilas ejaculari: </s> <s xml:id="echoid-s1022" xml:space="preserve">verùm debent eæ bombardæ farciri <lb/>ſquammis ferri, vel alterius metalli, lapidibus vel cate-<lb/>nis: </s> <s xml:id="echoid-s1023" xml:space="preserve">ſic enim mirabiles effectus patrant in oppugnan-<lb/>tes, & </s> <s xml:id="echoid-s1024" xml:space="preserve">in eos qui ſcalis admotis in murum aſcendunt. <lb/></s> <s xml:id="echoid-s1025" xml:space="preserve">Pila majorum bombardarum vires ſuas exeret, quum <lb/>foſſa repleta fuerit aceruis lapidum: </s> <s xml:id="echoid-s1026" xml:space="preserve">pilâ enim aceruos <lb/>illos feriente, lapides hinc atque hinc diſiecti innume-<lb/>ros oppugnantium neci dabunt. </s> <s xml:id="echoid-s1027" xml:space="preserve">Hæc etíam major <lb/>pila conducet ad rumpendas foſſas tranſuerſas, (Galli <lb/>tranchees,) & </s> <s xml:id="echoid-s1028" xml:space="preserve">alia machinamenta, quæ ab hoſtibus in <lb/>arcis foſſa parantur. </s> <s xml:id="echoid-s1029" xml:space="preserve">Præterea, ſi cortina ſit longitudi-<lb/>nis mediocris, & </s> <s xml:id="echoid-s1030" xml:space="preserve">apta ad vſum minorum bombarda-<lb/>rum, certum eſt ipſarum fulminationes, perniciem ho-<lb/>ſtium eſſe, & </s> <s xml:id="echoid-s1031" xml:space="preserve">fulcrum ipſius arcis: </s> <s xml:id="echoid-s1032" xml:space="preserve">quia, in omni op-<lb/>pugnatione, hoſtes ſeſe ſub cortina ſubdunt cum foſ-<lb/>ſis tranſuerſis, diruendo murum extrinſecum, vel im-<lb/>plendo ipſam foſſam, vt opera ligonis ſubuertendo <lb/>cortinam vel propugnaculum, ſibi ſcalam & </s> <s xml:id="echoid-s1033" xml:space="preserve">aſcenſum <lb/>parent ad ſaliendum in ipſam arcem.</s> <s xml:id="echoid-s1034" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1035" xml:space="preserve">Aqua in foſſa vtilis eſt, quum arx in eo loco ſita eſt, <lb/>qui pleroſq; </s> <s xml:id="echoid-s1036" xml:space="preserve">hoſtes in vicinia habet. </s> <s xml:id="echoid-s1037" xml:space="preserve">Tunc enim aqua <pb o="94" file="0094" n="116" rhead=""/> hoc arci beneficium confert, ne improuisò noctu per <lb/>ſcalas expugnari poſſit. </s> <s xml:id="echoid-s1038" xml:space="preserve">Conducit item minoribus ar-<lb/>cibus, quæ non poſſunt intra ſe tot milites capere, vt <lb/>ſatis ſint ad eruptiones faciendas pro arcis defenſione. <lb/></s> <s xml:id="echoid-s1039" xml:space="preserve">(Galli fairx ſortics.) </s> <s xml:id="echoid-s1040" xml:space="preserve">Aſt in arcibus majoribus, in qui-<lb/>bus eſt gens ſatis numeroſa ad eruptiones militares fa-<lb/>ciendas, ſiccam foſſam eſſe expediret, quia in ipſa ſpa-<lb/>tium adhuc eſſet ad receſſus faciendos, & </s> <s xml:id="echoid-s1041" xml:space="preserve">præterea cõ-<lb/>moda eſſet ad exeundum pro ipſius foſſæ defenſione, <lb/>ſicq́; </s> <s xml:id="echoid-s1042" xml:space="preserve">faciliùs poſſent amoueri ruinæ ab oppugnatione <lb/>hoſtili factæ, ne ſcalam hoſti præberent ad introitum <lb/>in arcem, vel ne hoſtis illis ruderibus coaceruatis vte-<lb/>retur pro lorica vel pro foſſa. </s> <s xml:id="echoid-s1043" xml:space="preserve">Foſſa abſque aqua præ-<lb/>bet adhuc aliud beneficium, quoties ſcilicet eam ho-<lb/>ſtis faſciculis lignorum implet, ad pontem ſibi in ar-<lb/>cem parandum: </s> <s xml:id="echoid-s1044" xml:space="preserve">quia ſic ab obſeſſis facilè poſſunt li-<lb/>gna exuri. </s> <s xml:id="echoid-s1045" xml:space="preserve">Quòd ſi aqua ineſſet, ignis vis impedire-<lb/>tur, & </s> <s xml:id="echoid-s1046" xml:space="preserve">foſſa faciliùs ab hoſte faſcibus lignorum imple-<lb/>retur. </s> <s xml:id="echoid-s1047" xml:space="preserve">Nocumento eſt etiam aqua tempore hiberno: </s> <s xml:id="echoid-s1048" xml:space="preserve"><lb/>ea enim congelata, facilior redditur in murum aſcen-<lb/>ſus. </s> <s xml:id="echoid-s1049" xml:space="preserve">Item foſſa, ſicca exiſtens, aliud beneficium imper-<lb/>tiret: </s> <s xml:id="echoid-s1050" xml:space="preserve">ſi enim milites ad velitationem, vel ad aliud ne-<lb/>gotium egreſſi eſſent, cogerenturq́;</s> <s xml:id="echoid-s1051" xml:space="preserve">, ob magnam ho-<lb/>ſtium impreſſionem, retro cedere, & </s> <s xml:id="echoid-s1052" xml:space="preserve">pons verſatilis ne-<lb/>ceſſariò eleuatus eſſet, (Galli dicunt pont ſcuis, quem <lb/>nos verſatilem diximus,) poſſentij in foſſam ſalire, & </s> <s xml:id="echoid-s1053" xml:space="preserve"><lb/>in ea ſaluari. </s> <s xml:id="echoid-s1054" xml:space="preserve">Sumitur & </s> <s xml:id="echoid-s1055" xml:space="preserve">alia vtilitas è foſſa ſic-<lb/>ca: </s> <s xml:id="echoid-s1056" xml:space="preserve">ſæpe enim accidit, tempore belli, vt <lb/>pecora totius agri in foſſis ab <lb/>hoſtilibus rapinis <lb/>tuta ſint.</s> <s xml:id="echoid-s1057" xml:space="preserve"/> </p> <pb o="95" file="0095" n="117"/> <figure> <image file="0095-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0095-01"/> </figure> <p> <s xml:id="echoid-s1058" xml:space="preserve">Quid conſiderandum ſit ei, qui à <lb/>Principe ſuo electus eſt ad defen <lb/>ſionem ſeu propugnationem ar-<lb/>cis alicujus.</s> <s xml:id="echoid-s1059" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div37" type="section" level="1" n="32"> <head xml:id="echoid-head39" xml:space="preserve">CAPVT TERTIVM.</head> <p> <s xml:id="echoid-s1060" xml:space="preserve"><emph style="sc">MVlta</emph> ſunt conſideranda & </s> <s xml:id="echoid-s1061" xml:space="preserve">perpenden-<lb/>da ei, qui à Principe ſuo electus eſt ad de <lb/>fenſionem, propugnationem, & </s> <s xml:id="echoid-s1062" xml:space="preserve">tutelam <lb/>ciuitatis alicujus vel arcis. </s> <s xml:id="echoid-s1063" xml:space="preserve">Hucuſq; </s> <s xml:id="echoid-s1064" xml:space="preserve">affa-<lb/>tim diſſeruimus de ſitu, fabrica, & </s> <s xml:id="echoid-s1065" xml:space="preserve">muni-<lb/>tione arciũ: </s> <s xml:id="echoid-s1066" xml:space="preserve">ſupereſt vt de iis conſeruandis agatur. </s> <s xml:id="echoid-s1067" xml:space="preserve">De <lb/>cura autẽ & </s> <s xml:id="echoid-s1068" xml:space="preserve">diligentia, quã adhibere debet arcis præfe-<lb/>ctus, vt arx muniatur rebus neceſſariis ad ſui conſerua-<lb/>tionẽ, vt cõmeatus abundet, tum ad plebis, tum ad præ <lb/>ſidiariorum militum victum, vt reliquis rebus neceſſa-<lb/>riis arx in tempore muniatur, in præſentia non dicam, <lb/>quia neminem latet, arces & </s> <s xml:id="echoid-s1069" xml:space="preserve">ciuitates aliâs inexpugna-<lb/>biles, in hoſtium poteſtatem venturas, quotiescumque <lb/>deſtituuntur rebus ad vitam ſuſtentandam neceſſariis. <lb/></s> <s xml:id="echoid-s1070" xml:space="preserve">Nec ſperandum eſt, ciuitates & </s> <s xml:id="echoid-s1071" xml:space="preserve">arces, quum obſideri <lb/>cœperint, poſſe ſibi commeatum accerſere, ſéque exo-<lb/>nerare perſonis inutilibus, & </s> <s xml:id="echoid-s1072" xml:space="preserve">fruges conſumere natis. </s> <s xml:id="echoid-s1073" xml:space="preserve"><lb/>Hoc enim eſt valde difficile, & </s> <s xml:id="echoid-s1074" xml:space="preserve">exitus fallax. </s> <s xml:id="echoid-s1075" xml:space="preserve">Exẽplo fue <lb/>re, noſtris his temporibus, Florẽtia & </s> <s xml:id="echoid-s1076" xml:space="preserve">Siena, quæ quum <lb/>tempeſtiuè ſibi non conſuluiſſent, tandem hiſce reme- <pb o="96" file="0096" n="118" rhead=""/> diis volentes vti, mirum eſt quàm paruo ſibi fuerint <lb/>adiumento, & </s> <s xml:id="echoid-s1077" xml:space="preserve">cum quibus anguſtiis ac miſeriis vix, ac <lb/>ne vix quidem, minimam partem eorum quæ ſpera-<lb/>uerant, conſequuti ſunt. </s> <s xml:id="echoid-s1078" xml:space="preserve">Verùm hæc recenſere miſe-<lb/>randum potiùs eſſet quâm neceſſarium. </s> <s xml:id="echoid-s1079" xml:space="preserve">Subſidia igi-<lb/>tur illa & </s> <s xml:id="echoid-s1080" xml:space="preserve">commeatus in tempore fieri debent, vt par <lb/>eſt. </s> <s xml:id="echoid-s1081" xml:space="preserve">Dicamus jam de arcium præſidio. </s> <s xml:id="echoid-s1082" xml:space="preserve">De numero <lb/>præſidiariorum ſuprà etiam egimus, quum conſului-<lb/>mus multo majorem numerum militum eſſe debere <lb/>eo qui idoneus videretur ad loci defenſionem, tum vt <lb/>eruptiones in obſidentes faciliùs fieri poſſint, tum e-<lb/>tiam quia in locis obſeſſis, & </s> <s xml:id="echoid-s1083" xml:space="preserve">aduerſa valetudine à va-<lb/>riis incommoditatibus contracta, & </s> <s xml:id="echoid-s1084" xml:space="preserve">ferro, multi per-<lb/>eunt. </s> <s xml:id="echoid-s1085" xml:space="preserve">Conſulerem ergo vt ad defenſionem ciuitatum <lb/>& </s> <s xml:id="echoid-s1086" xml:space="preserve">arcium, pro quibuſlibet mille paſſibus mille milites <lb/>conſcriberentur, vel etiam major numerus, <lb/>pro propugnaculorum magnitu-<lb/>dine, & </s> <s xml:id="echoid-s1087" xml:space="preserve">aliorum arcis <lb/>locorum.</s> <s xml:id="echoid-s1088" xml:space="preserve"/> </p> <figure> <image file="0096-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0096-01"/> </figure> <pb o="97" file="0097" n="119"/> <figure> <image file="0097-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0097-01"/> </figure> <p> <s xml:id="echoid-s1089" xml:space="preserve">Demodo cuſtodiendiac con-<lb/>ſeruandi arces.</s> <s xml:id="echoid-s1090" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div38" type="section" level="1" n="33"> <head xml:id="echoid-head40" xml:space="preserve">CAPVT QVARTVM.</head> <p> <s xml:id="echoid-s1091" xml:space="preserve">DE militibus dictum eſt, jam agamus de <lb/>numero & </s> <s xml:id="echoid-s1092" xml:space="preserve">qualitate bombardarum. </s> <s xml:id="echoid-s1093" xml:space="preserve">Eæ <lb/>tot debent eſſe quot neceſſariæ ſunt ad <lb/>defenſionem propugnaculorum, plana-<lb/>rum formarum, vallorum prominen-<lb/>tium, & </s> <s xml:id="echoid-s1094" xml:space="preserve">aliorum locorum. </s> <s xml:id="echoid-s1095" xml:space="preserve">Verùm deiis canon com-<lb/>modè non poteſt dari: </s> <s xml:id="echoid-s1096" xml:space="preserve">quia, prout ſeſe occaſio offert, <lb/>varia etiam ſunt conſilia: </s> <s xml:id="echoid-s1097" xml:space="preserve">aliquando plures, aliquando <lb/>pauciores bombardæ arci imponuntur, habita ratio-<lb/>ne vitium hoſtis, & </s> <s xml:id="echoid-s1098" xml:space="preserve">abundantia vel penuria commea-<lb/>tus. </s> <s xml:id="echoid-s1099" xml:space="preserve">Vnaquæq; </s> <s xml:id="echoid-s1100" xml:space="preserve">bombarda inſtructa debet eſſe ſuis pro-<lb/>priis inſtrumentis & </s> <s xml:id="echoid-s1101" xml:space="preserve">aliis rebus neceſſariis, pilis, pulue-<lb/>re, quantum ſatis eſt. </s> <s xml:id="echoid-s1102" xml:space="preserve">Præterea laudarem vt illic eſſet <lb/>omne genus inſtrumentorũ, quæ faciunt ad oppugna-<lb/>tionem propulſandam. </s> <s xml:id="echoid-s1103" xml:space="preserve">Neceſſarium eſt & </s> <s xml:id="echoid-s1104" xml:space="preserve">inibi omne <lb/>genus ferramentorum: </s> <s xml:id="echoid-s1105" xml:space="preserve">carbones in magna quantitate, <lb/>cum aliis rebus quæ ad ignes artificiales componen-<lb/>dos ſunt commodæ: </s> <s xml:id="echoid-s1106" xml:space="preserve">ad hæc omnis materia è qua pul-<lb/>uis tormentarius conficitur, piſtrinorum omne genus, <lb/>inſtrumenta ferrea & </s> <s xml:id="echoid-s1107" xml:space="preserve">alia vtenſilia foſſorum, (Galli <lb/>pionnicrs,) vt ligones, ſarcula, bidentes, palæ, rutra, fur-<lb/>cæ, marræ, paſtina, irpices, mergæ, runcinæ, gerulæ, <lb/>vangæ, corbes, ſportulæ, & </s> <s xml:id="echoid-s1108" xml:space="preserve">id genus alia, quæ, faciunt <pb o="98" file="0098" n="120" rhead=""/> ad eruendam & </s> <s xml:id="echoid-s1109" xml:space="preserve">portandam terram, ligna, faſces ra-<lb/>mulorum: </s> <s xml:id="echoid-s1110" xml:space="preserve">in ſumma quidquid facit ad aggeres ex-<lb/>ſtruendos, &</s> <s xml:id="echoid-s1111" xml:space="preserve">, ſi vſu veniat, ad ruinas ab hoſte bombar-<lb/>dis factas reparandas. </s> <s xml:id="echoid-s1112" xml:space="preserve">Præterea magnus numerus plu-<lb/>teorum, (Gal. </s> <s xml:id="echoid-s1113" xml:space="preserve">gabions,) quibus tamen non multum fi-<lb/>dendum, ſi eis vtaris ad conſeruationem bombarda-<lb/>rum, quamuis ſint vaſti & </s> <s xml:id="echoid-s1114" xml:space="preserve">bene impleti: </s> <s xml:id="echoid-s1115" xml:space="preserve">experientia <lb/>enim docuit illis non multum ſecuritatis ineſſe: </s> <s xml:id="echoid-s1116" xml:space="preserve">verùm <lb/>perneceſſarij ſunt ad nos operiendos, præcipuè vbi ag-<lb/>geres vel aliæ munitiones incipiunt exſtrui. </s> <s xml:id="echoid-s1117" xml:space="preserve">Debet <lb/>item arx inſtructa eſſe omni genere artificum, quales <lb/>funt fabri lignarij, ferrarij, murarij, lapicidæ, & </s> <s xml:id="echoid-s1118" xml:space="preserve">id ge-<lb/>nus alij. </s> <s xml:id="echoid-s1119" xml:space="preserve">Debet etiam in arce eſſe magnus numerus ar-<lb/>morum, & </s> <s xml:id="echoid-s1120" xml:space="preserve">omnium generum, vt poſſint eis armari <lb/>plebs, & </s> <s xml:id="echoid-s1121" xml:space="preserve">lixæ, vbi ſeſe occaſio & </s> <s xml:id="echoid-s1122" xml:space="preserve">neceſſitas offerret: <lb/></s> <s xml:id="echoid-s1123" xml:space="preserve">namq; </s> <s xml:id="echoid-s1124" xml:space="preserve">non minor eſt virtus quàm quærere parta tueri. </s> <s xml:id="echoid-s1125" xml:space="preserve"><lb/>Præterea debet præfectus arcis eſſe valdè attentus & </s> <s xml:id="echoid-s1126" xml:space="preserve">ſa-<lb/>gax ad perſpiciendas & </s> <s xml:id="echoid-s1127" xml:space="preserve">præuidendas hoſtium fraudes <lb/>& </s> <s xml:id="echoid-s1128" xml:space="preserve">furta: </s> <s xml:id="echoid-s1129" xml:space="preserve">præcipuè vbi hoſtis ita vicinus eſt, vt vna no-<lb/>cte tibi immineat, & </s> <s xml:id="echoid-s1130" xml:space="preserve">ſcalarum ope tibi damnum affe-<lb/>rat. </s> <s xml:id="echoid-s1131" xml:space="preserve">Horum enim exempla quotidie exſtant, quorum <lb/>teſtes probati ſunt Alba, Caſalis & </s> <s xml:id="echoid-s1132" xml:space="preserve">Torchiara in præ-<lb/>teritis bellis Pedemontis & </s> <s xml:id="echoid-s1133" xml:space="preserve">Parmæ. </s> <s xml:id="echoid-s1134" xml:space="preserve">Debet etiam præ-<lb/>fectus arcis ſumma diligentia vti, in collocan dis excu-<lb/>biis, & </s> <s xml:id="echoid-s1135" xml:space="preserve">ſtationibus, ſeu corporibus præſidiariis (Galli, <lb/>corps de garde:) </s> <s xml:id="echoid-s1136" xml:space="preserve">numerus enim ordinarius non ſatis eſt, <lb/>vbinobis res eſt cum hoſte audaci, qui libenter fortu-<lb/>nam tẽtat, quiq́; </s> <s xml:id="echoid-s1137" xml:space="preserve">delectatur impreſſionibus nocturnis, <lb/>quæ, vbi prudenter adminiſtrantur, maximos gignunt <lb/>effectus. </s> <s xml:id="echoid-s1138" xml:space="preserve">Conſulerem etiam, vt noſter præfectus octo <lb/>aut decem equites emitteret ad eam partem à qua ho- <pb o="99" file="0099" n="121" rhead=""/> ſtis expectatur, qui viam obſeruarent, ne quidquam <lb/>ſuperuenire poſſet de quo ante certior factus nõ eſſet, <lb/>quo poſſet tutiùs ſe ab hoſtili impreſſione defendere. <lb/></s> <s xml:id="echoid-s1139" xml:space="preserve">Quod verò attinet ad fraudes, quas à noſtris ipſis mi-<lb/>litibus patimur, laudo in hoc prudentiam, qua vſi ſunt <lb/>Galli in Pedemonte, & </s> <s xml:id="echoid-s1140" xml:space="preserve">in bellis Parmenſi & </s> <s xml:id="echoid-s1141" xml:space="preserve">Senenſi, <lb/>ne quis ſcilicet gnarus ſit quo in loco collocandus erit, <lb/>nec vbi debeat excubias agere. </s> <s xml:id="echoid-s1142" xml:space="preserve">Præterea ſingulis no-<lb/>ctibus mutentur cuſto diæ, (Galli fcs gardes:) </s> <s xml:id="echoid-s1143" xml:space="preserve">ſingulis ho-<lb/>ris ac momentis inſpiciantur tũ cuſtodiæ, tum excubiæ, <lb/>à militibus ad id electis. </s> <s xml:id="echoid-s1144" xml:space="preserve">Galli vocant vondes. </s> <s xml:id="echoid-s1145" xml:space="preserve">Nollem <lb/>etiam eum, cujus curæ & </s> <s xml:id="echoid-s1146" xml:space="preserve">fidei demandata eſt tutela <lb/>alicujus loci, concedere vt ſui milites negotia tracta-<lb/>rent, colloquerentur, & </s> <s xml:id="echoid-s1147" xml:space="preserve">familiaritatem inirent cum <lb/>hoſtibus, vt ſæpe factitatum eſt, præcipuè inter Italos: </s> <s xml:id="echoid-s1148" xml:space="preserve"><lb/>immò hæc omnia penitus prohibere, curareq́; </s> <s xml:id="echoid-s1149" xml:space="preserve">vt qui-<lb/>libet ex ſuis animum hoſtilem erga hoſtes gerat. </s> <s xml:id="echoid-s1150" xml:space="preserve">Ca-<lb/>ueat etiam ne crebrò tubicines & </s> <s xml:id="echoid-s1151" xml:space="preserve">tympaniſtæ hoſtium <lb/>arcem ingrediantur: </s> <s xml:id="echoid-s1152" xml:space="preserve">plerumque enim accidit vt id <lb/>munus exercentes, viri ſint aſtuti, & </s> <s xml:id="echoid-s1153" xml:space="preserve">ad nocendum pa-<lb/>rati, ſicut experientia docuit in bello Parmenſi, quum <lb/>Torchiara ab hoſtibus capta eſt. </s> <s xml:id="echoid-s1154" xml:space="preserve">Quum enim illuc <lb/>frequenter veniret tympaniſtes quidam, illi licuit in-<lb/>ſpicere aggeres & </s> <s xml:id="echoid-s1155" xml:space="preserve">valla, eorumq́; </s> <s xml:id="echoid-s1156" xml:space="preserve">altitudinem metiri, vn-<lb/>de ſequuta eſt loci illius captura, cum morte Principis <lb/>Macedoniæ, qui illic imperabat. </s> <s xml:id="echoid-s1157" xml:space="preserve">Nolo etiam retice-<lb/>re, quantum inuidiæ, faſtidij, & </s> <s xml:id="echoid-s1158" xml:space="preserve">laboris ſuſtineant ij, <lb/>qui Principibus inſeruiunt, bellicas artes profitentes: </s> <s xml:id="echoid-s1159" xml:space="preserve"><lb/>ſed præcipuè ij qui Mathematicarum diſciplinarum <lb/>ope, artem profitentur muniendi, & </s> <s xml:id="echoid-s1160" xml:space="preserve">exſtruendi arces <lb/>& </s> <s xml:id="echoid-s1161" xml:space="preserve">propugnacula. </s> <s xml:id="echoid-s1162" xml:space="preserve">Hoc aliquando accidit, quia Prin- <pb o="100" file="0100" n="122" rhead=""/> ceps vel Imperator jubebit te loci alicujus tutelam ac <lb/>defenſionem ſuſcipere: </s> <s xml:id="echoid-s1163" xml:space="preserve">quem locum tu certò cogno-<lb/>ſces non poſſe defendi. </s> <s xml:id="echoid-s1164" xml:space="preserve">Tu verò, qui ſemper hono-<lb/>rem & </s> <s xml:id="echoid-s1165" xml:space="preserve">famam conſeruare voluiſti, ne aliquando incaſ-<lb/>ſum rationem reddere cogaris de arce amiſſa, recuſa-<lb/>bis imperata exequi. </s> <s xml:id="echoid-s1166" xml:space="preserve">Hinc ſequitur alienatus & </s> <s xml:id="echoid-s1167" xml:space="preserve">offen-<lb/>ſus animus Principis tui, neque ſolùm Principis, ſed <lb/>etiam totius vulgi, qui te vt puſillanimem calumnia-<lb/>bitur:</s> <s xml:id="echoid-s1168" xml:space="preserve">ita vt mihi ſatius videatur militem ſtrenuum im-<lb/>peratis Domini ſui potiùs acquieſcere, vitæq́; </s> <s xml:id="echoid-s1169" xml:space="preserve">ſuæ peri-<lb/>culum adire, modò in eo negotio ſe fortem ac diligen-<lb/>tem præbeat, quàm abnuere juſſa exequi. </s> <s xml:id="echoid-s1170" xml:space="preserve">Poteſt qui-<lb/>dem ac debet miles noſter Domino ſuo palàm facere, <lb/>locum illum nullo pacto defendi poſſe, nihilominus <lb/>ſe paratum eſſe ac velle illi morem gerere, etiam ſi id <lb/>fiat cum certo vitæ ſuæ periculo. </s> <s xml:id="echoid-s1171" xml:space="preserve">Tunc ſi Princeps vel <lb/>Imperator ſit ea prudentia qua decet, non tam parui <lb/>faciet vitam ſuorum, vt eam velit temere & </s> <s xml:id="echoid-s1172" xml:space="preserve">abſque fru-<lb/>ctu periculo objicere, immò magni faciet militem <lb/>ſuum, ejusq́; </s> <s xml:id="echoid-s1173" xml:space="preserve">fidem ac fortitudinem præmio aliquo de-<lb/>corabit. </s> <s xml:id="echoid-s1174" xml:space="preserve">Quum autem in hoc capite dixerim de iis <lb/>quæ mihi ex vſu eſſe viſa ſunt ad tutelam & </s> <s xml:id="echoid-s1175" xml:space="preserve">defenſio-<lb/>nem alicujus arcis, necnon & </s> <s xml:id="echoid-s1176" xml:space="preserve">de commeatu rerum ne-<lb/>ceſſariarum in eam immittendo, in ſequenti capite à <lb/>me dicetur quo pacto ſe gerere debeat is <lb/>qui ciuitatem vel arcem oppu-<lb/>gnare volet, immò & </s> <s xml:id="echoid-s1177" xml:space="preserve"><lb/>expugnare.</s> <s xml:id="echoid-s1178" xml:space="preserve"/> </p> <pb o="101" file="0101" n="123"/> <figure> <image file="0101-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0101-01"/> </figure> <p> <s xml:id="echoid-s1179" xml:space="preserve">Quo pacto ſe gerat Imperator, qui <lb/>viderit arcem aliquam expugna-<lb/>ri non poſſe:</s> <s xml:id="echoid-s1180" xml:space="preserve">ac quomodo eam <lb/>ſit obſeſſurus.</s> <s xml:id="echoid-s1181" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div39" type="section" level="1" n="34"> <head xml:id="echoid-head41" xml:space="preserve">CAPVT QVINTVM.</head> <p> <s xml:id="echoid-s1182" xml:space="preserve">QV <emph style="sc">VM</emph> Imperator, (Galli vocant E<unsure/>circ@al, <lb/>qui inſtituerit ciuitatem aliquam vel ar-<lb/>cem in ſuam poteſtatem redigere, certò <lb/>cognouerit id viac expugnatione fieri <lb/>non poſſe, conſtitueritq́; </s> <s xml:id="echoid-s1183" xml:space="preserve">eam obſidione <lb/>cingere, vt tandem poſt magnum temporis interual-<lb/>lum voti compos fiat, primò debebit prudenter & </s> <s xml:id="echoid-s1184" xml:space="preserve">at-<lb/>tentè, & </s> <s xml:id="echoid-s1185" xml:space="preserve">poſt crebras totius ſitus inſpectiones, eligere <lb/>locum in quo caſtrametaturus eſt, & </s> <s xml:id="echoid-s1186" xml:space="preserve">exercitus ſedes <lb/>fixurus. </s> <s xml:id="echoid-s1187" xml:space="preserve">Sed inprimis locum debet eligere vbi aër ſit <lb/>purus, non calamitoſus, in memoriã reuocans id quod <lb/>accidit Domino de Lautrect in obſidione Neapolita-<lb/>na, qui, quòd in hac electione peccaſſet, non tantùm <lb/>non potuitad finem perducere id quod inſtituerat, ve-<lb/>rùm & </s> <s xml:id="echoid-s1188" xml:space="preserve">exercitus ſui & </s> <s xml:id="echoid-s1189" xml:space="preserve">vitæ propriæ jacturam fecit, cũ <lb/>ingenti ſtrage nobilitatis Gallicanæ, vt nemini notum <lb/>non eſt. </s> <s xml:id="echoid-s1190" xml:space="preserve">Eligat etiam, quantum fieri poterit, locum <lb/>commodum ad aquationem, lignationem, & </s> <s xml:id="echoid-s1191" xml:space="preserve">rerum <lb/>ad victum neceſſariarum comportationem. </s> <s xml:id="echoid-s1192" xml:space="preserve">Viden-<lb/>dum etiam vt tutus ſit à bombardis hoſtilibus, quan- <pb o="102" file="0102" n="124" rhead=""/> <pb file="0102_0103" n="125"/> <pb o="103" file="0103" n="126" rhead=""/> <anchor type="figure" xlink:label="fig-0103-01a" xlink:href="fig-0103-01"/> <pb o="104" file="0104" n="127" rhead=""/> tum poſſit. </s> <s xml:id="echoid-s1193" xml:space="preserve">Silocus obſidendus magnus ſit, & </s> <s xml:id="echoid-s1194" xml:space="preserve">mu- nitus magno numero militum, præcipuè equitum ad eruptiones & </s> <s xml:id="echoid-s1195" xml:space="preserve">velitationes crebrò faciendas, ſubitò de- bet curare, ita muniri caſtra, vt per ſe poſſint viri- bus hoſtium obſiſtere. </s> <s xml:id="echoid-s1196" xml:space="preserve">Quo facto priuabit hoſtes omni commoditate, velutiaqua, & </s> <s xml:id="echoid-s1197" xml:space="preserve">aliis rebus, quæ il- los juuare poſſunt, eosq́; </s> <s xml:id="echoid-s1198" xml:space="preserve">ad extremam neceſſitatem rediget. </s> <s xml:id="echoid-s1199" xml:space="preserve">Præterea euentus ſæpe probauit, rem eſſe pe- riculoſiſſimam, ſi quis exercitum diuidat, vel eum ni- mis imminuat, quũ caſtrametatur prope ciuitatem ho ſtilem, præcipuè ſi in ea ſint magnæ vires, & </s> <s xml:id="echoid-s1200" xml:space="preserve">milites ſtrenui, quemadmodum accidit in obſidione Floren- tiæ. </s> <s xml:id="echoid-s1201" xml:space="preserve">Quum enim hoſtes bipartitò diuiſiſſent exerci- tum, parte cis Arnum, Aquilonem verſus, collocata, in qua erant Germani, altera verò parte Meridiem ver- ſus, in qua erat Imperator ipſe, cum præcipuis exerci- tus viribus, ciuitas illa, vt ſe tanta moleſtia liberaret, noctu impreſſionem fecit in copias Germanorum, eo ardore, vt niſi confuſio conſequuta eſſet inter eos qui impreſſionem faciebant, totum agmen Germanorum deletum erat, & </s> <s xml:id="echoid-s1202" xml:space="preserve">ab ea parte ciuitas obſidione libera- batur. </s> <s xml:id="echoid-s1203" xml:space="preserve">Credo igitur ſecurius eſſe & </s> <s xml:id="echoid-s1204" xml:space="preserve">facilius, ciuitatem obſidendam premere, per exſtructionem propugna- culorumſeu vallorum eminẽtium, vt fieri cœptum eſt in vltimis bellis Mirandulæ & </s> <s xml:id="echoid-s1205" xml:space="preserve">Sienæ, conſiderando diligenter omnes vias & </s> <s xml:id="echoid-s1206" xml:space="preserve">omnia loca per quæ oppida- nis ſuppetias afferre poſſint amici, & </s> <s xml:id="echoid-s1207" xml:space="preserve">in ſingulis locis aggeres vel valla exſtruere: </s> <s xml:id="echoid-s1208" xml:space="preserve">vel potiùs tam prope ciui- tatem ſuas figere ſedes, vt cum quatuor vel quinque vallis tota ciuitas circumcludi poſſit. </s> <s xml:id="echoid-s1209" xml:space="preserve">Nollem ſic ex- ſtrui hæc valla, vt, præ paruitate, nimis debilia eſſent, <pb o="105" file="0105" n="128" rhead=""/> nec vellem ita ſita eſſe, vt alterum alteri ſuppetias ferre nequiret. </s> <s xml:id="echoid-s1210" xml:space="preserve">Verùm qua forma & </s> <s xml:id="echoid-s1211" xml:space="preserve">quomodo vellem ea exſtrui infrà à nobis deſignatum eſt decimaſexta figura.</s> <s xml:id="echoid-s1212" xml:space="preserve"/> </p> <div xml:id="echoid-div39" type="float" level="2" n="1"> <figure xlink:label="fig-0102-01" xlink:href="fig-0102-01a"> <image file="0102-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0102-01"/> </figure> <figure xlink:label="fig-0103-01" xlink:href="fig-0103-01a"> <image file="0103-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0103-01"/> </figure> </div> <p> <s xml:id="echoid-s1213" xml:space="preserve">Deinde cum reliquo exercitu ſtabit inloco vnde fa-<lb/>cilè poſſit ſuppetias ſuis ferre:</s> <s xml:id="echoid-s1214" xml:space="preserve">vel etiam cum parte exer-<lb/>citus, attentè priùs perpenſis hoſtiũ viribus, ac cum iis <lb/>bombardis, quæ commodæ videbuntur, in ſuam po-<lb/>teſtatem rediget totum agrum circumjacentem, præci-<lb/>puè loca expugnatu facilia: </s> <s xml:id="echoid-s1215" xml:space="preserve">vnde ſibi magnam conci-<lb/>liabit commoditatem propter commeatum. </s> <s xml:id="echoid-s1216" xml:space="preserve">ſic enim <lb/>non ſolummodo exercitum ſuum nutriet, ſed & </s> <s xml:id="echoid-s1217" xml:space="preserve">obſeſ-<lb/>ſis auferet omnem ſuppetiarum ſpem, magnumq́; </s> <s xml:id="echoid-s1218" xml:space="preserve">no-<lb/>men exercitui ſuo comparabit: </s> <s xml:id="echoid-s1219" xml:space="preserve">ita vt iſtius tractus in-<lb/>colæ nec reſiſtere, nec etiam mutire audeant, ſed vel <lb/>amore, veltimore, in officio continebuntur.</s> <s xml:id="echoid-s1220" xml:space="preserve"/> </p> <figure> <image file="0105-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0105-01"/> </figure> <p> <s xml:id="echoid-s1221" xml:space="preserve">Quomodo ſegeret Imperator, vbi <lb/>viderit arcem expugnari poſſe.</s> <s xml:id="echoid-s1222" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div41" type="section" level="1" n="35"> <head xml:id="echoid-head42" xml:space="preserve">CAPVT SEXTVM.</head> <p> <s xml:id="echoid-s1223" xml:space="preserve"><emph style="sc">DIximvs</emph> ſuperiori capite quanti pon-<lb/>deris ſiteligere locum ſtationis commo-<lb/>dum ac ſecurum. </s> <s xml:id="echoid-s1224" xml:space="preserve">Supereſt vt hoc ſexto <lb/>dicam, quid fieri ſoleat ac debeat vbi Im <lb/>perator viderit poſſe vi expugnari ciui-<lb/>tatem vel arcem. </s> <s xml:id="echoid-s1225" xml:space="preserve">Primò mittendi ſunt cum magiſtro <lb/>militiæ (Galli maiſtre de camp,) milites exercitati, cum <pb o="106" file="0106" n="129" rhead=""/> <pb file="0106_0107" n="130"/> <pb o="107" file="0107" n="131" rhead=""/> <anchor type="figure" xlink:label="fig-0107-01a" xlink:href="fig-0107-01"/> <pb o="108" file="0108" n="132" rhead=""/> aliis numero ſufficienti, qui attentè poſſint inſpicere & </s> <s xml:id="echoid-s1226" xml:space="preserve">notare ambitum ciuitatis, ſitum ipſius, & </s> <s xml:id="echoid-s1227" xml:space="preserve">quæ pars commodior ſit ad collocandas bombardas foſſarum tranſuerſarum ope, (Galli tranchccs.) </s> <s xml:id="echoid-s1228" xml:space="preserve">Debet autem in primis aduertere, vt terra ſit ejus generis, quæ facilè poſſit tractari, tum ad foſſas ducendas, tum ad alia o- pera militaria, quæ neceſſaria ſunt quo ſe ab hoſtibus tueatur. </s> <s xml:id="echoid-s1229" xml:space="preserve">Verùm impoſſibile eſt exactè recognoſcere, vel interdiu vel noctu omnia ea quæ pertinent ad eam ciuitatem vel arcem: </s> <s xml:id="echoid-s1230" xml:space="preserve">quia interdiu hoſtes non ſinent id liberè fieri, ſi ſaltem animis valeant: </s> <s xml:id="echoid-s1231" xml:space="preserve">noctu verò, pro- pter obſcuritatem nequimus metiri latera nec foſſam, nec alia pleraque inſpicere, quæ neceſſaria ſunt ei qui exactè & </s> <s xml:id="echoid-s1232" xml:space="preserve">conſideratè ſe vult ad eam expugnationem accingere. </s> <s xml:id="echoid-s1233" xml:space="preserve">Sed hoc bene & </s> <s xml:id="echoid-s1234" xml:space="preserve">commodiſſimè fiet, quan- do foſſas tuas perduxeris vſque ad ciuitatis foſſam. </s> <s xml:id="echoid-s1235" xml:space="preserve">Illic ipſemet Imperator poterit commodè ſingula videre, & </s> <s xml:id="echoid-s1236" xml:space="preserve">certior fieri eorum omnium quæ reſcire deſiderat.</s> <s xml:id="echoid-s1237" xml:space="preserve"> De modo autem haſce foſſas tranſuerſas faciendi variæ ſunt opiniones. </s> <s xml:id="echoid-s1238" xml:space="preserve">nos, vt in hoc etiam lectoriſatisfacere- mus, varia earum genera deſignauimus, quæ commo- diora & </s> <s xml:id="echoid-s1239" xml:space="preserve">ſecuriora judicauimus, quæq́; </s> <s xml:id="echoid-s1240" xml:space="preserve">citiùs parari poſſunt. </s> <s xml:id="echoid-s1241" xml:space="preserve">Sed ante omnia recordetur Imperator, in illis foſſis loca ſtatuere, in quibus cum ſecuritate collocet corpora præſidiaria (corps de gazde) ita diſpoſita vt al- terum altero ſuppetias ferre poſſit. </s> <s xml:id="echoid-s1242" xml:space="preserve">Sint etiam in illis foſſis exitus, ſeu viæ per quas illinc exeatur, vt ex noſtris deſcriptionibus apparebit, ac etiam in decima ſeptima figura.</s> <s xml:id="echoid-s1243" xml:space="preserve"/> </p> <div xml:id="echoid-div41" type="float" level="2" n="1"> <figure xlink:label="fig-0106-01" xlink:href="fig-0106-01a"> <image file="0106-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0106-01"/> </figure> <figure xlink:label="fig-0107-01" xlink:href="fig-0107-01a"> <image file="0107-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0107-01"/> </figure> </div> <p> <s xml:id="echoid-s1244" xml:space="preserve">Hoc facto eliges locum ad locandas bombardas, <lb/>cum ſuis pluteis, reliquisq́; </s> <s xml:id="echoid-s1245" xml:space="preserve">inſtrumentis ad eas perti- <pb o="109" file="01090" n="133" rhead=""/> nentibus. </s> <s xml:id="echoid-s1246" xml:space="preserve">Poſtea bombardarum magiſter, (Maiſtix ou <lb/>Lapitainc de ſ’ artiſſeric) cum ſuis miniſtris, ſi ſint exer-<lb/>citati & </s> <s xml:id="echoid-s1247" xml:space="preserve">fortes, obibunt munia circa eas neceſſaria. <lb/></s> <s xml:id="echoid-s1248" xml:space="preserve">Solo, cui debebunt imponi bombardæ ad oppugna-<lb/>tionem faciendam, ſuperponentur optimi aſſeres, vel <lb/>etiam trabes benè læuigatæ, eritq́; </s> <s xml:id="echoid-s1249" xml:space="preserve">ſolum illud paulu-<lb/>lum pendens verſus feneſtras tormentarias, vt, poſtquã <lb/>bombardæ retroceſſerint, faciliùs ad ſuas feneſtras re-<lb/>ducantur. </s> <s xml:id="echoid-s1250" xml:space="preserve">Aſſeres autem illi vel trabes, impedient ne <lb/>tempore humido & </s> <s xml:id="echoid-s1251" xml:space="preserve">pluuioſo bombardæ ſeſe in hu-<lb/>mum defigant. </s> <s xml:id="echoid-s1252" xml:space="preserve">Plerique ſentiunt, bombardas non <lb/>debere longiùs centum quinquaginta paſſibus à mu-<lb/>ris oppugnandis abeſſe, ſi quidem ſitus id concederet. </s> <s xml:id="echoid-s1253" xml:space="preserve"><lb/>De bombardarum generibus nunc verba non faciam, <lb/>poſthac, vbilocus erit, de iis dicturus. </s> <s xml:id="echoid-s1254" xml:space="preserve">Hoc ſolùm dicã, <lb/>ex vſu hodierno, debere eſſe bombardas ſeu tormenta, <lb/>quæ pilas ejaculentur ſexaginta pondo, ita firmata, vt <lb/>non dubitandum ſit, quin, etiamſi continuè pilas eja-<lb/>culentur à mane ad veſperam, nihilominus remaneant <lb/>juſta & </s> <s xml:id="echoid-s1255" xml:space="preserve">firma. </s> <s xml:id="echoid-s1256" xml:space="preserve">Quo plura erunt tormenta bellica, & </s> <s xml:id="echoid-s1257" xml:space="preserve"><lb/>quo pluribus in locis murus quatietur, eo plus terroris <lb/>hoſti incutietur, & </s> <s xml:id="echoid-s1258" xml:space="preserve">expugnatio facilior reddetur: </s> <s xml:id="echoid-s1259" xml:space="preserve">præ-<lb/>cipuè ſi tranſuerſa & </s> <s xml:id="echoid-s1260" xml:space="preserve">decuſſatim poſſit oppugnatio fie-<lb/>ri: </s> <s xml:id="echoid-s1261" xml:space="preserve">ſed multo magis nos juuabit, ſi commodum ſit eri-<lb/>gere & </s> <s xml:id="echoid-s1262" xml:space="preserve">exſtruere vallum prominens ita elatum, vt illi ſit <lb/>aperta cortina. </s> <s xml:id="echoid-s1263" xml:space="preserve">Aduertendum eſt etiam, vt ejaculatio-<lb/>nes bombardarum continuæ ſint, nullumq́; </s> <s xml:id="echoid-s1264" xml:space="preserve">interual-<lb/>lum inter eas intercedat, ſi poſſibile ſit: </s> <s xml:id="echoid-s1265" xml:space="preserve">plurimum enim <lb/>intereſt, nullam hoſti requiem concedere: </s> <s xml:id="echoid-s1266" xml:space="preserve">nec noctu <lb/>etiam ab oppugnatione deſiſtendum eſt: </s> <s xml:id="echoid-s1267" xml:space="preserve">quod vt fa-<lb/>ciliùs fiat, inuenta ſunt optima media. </s> <s xml:id="echoid-s1268" xml:space="preserve">Foſſam tuam <pb o="110" file="0110" n="134" rhead=""/> <pb file="0110_0111" n="135"/> <pb o="111" file="0111" n="136" rhead=""/> <pb o="112" file="0112" n="137" rhead=""/> tranſuerſam, prope foſſam arcis duces, præcipuè ab ea parre ex qua fit oppugnatio. </s> <s xml:id="echoid-s1269" xml:space="preserve">Eliges ex vniuerſo exer citu magnum numerum ſclopetariorum, qui præter cæteros animis & </s> <s xml:id="echoid-s1270" xml:space="preserve">experientia valeant, qui tamen ſua corpora præſidiaria habeant vnà cum ſuo exitu:</s> <s xml:id="echoid-s1271" xml:space="preserve">eruntq́;</s> <s xml:id="echoid-s1272" xml:space="preserve"> ita locata hæc corpora, juxta noſtram deſcriptionem, vt pro lateribus etiam ſeruiant. </s> <s xml:id="echoid-s1273" xml:space="preserve">Horum autem ſclope- ti ejaculentur glandes duarum vnciarum. </s> <s xml:id="echoid-s1274" xml:space="preserve">Similes enim mirum in modum vexant propugnantes, præcipuè quum murus dirui incipit. </s> <s xml:id="echoid-s1275" xml:space="preserve">Quod autem hî dictũ eſt, id præcedens decima octaua figura ob oculos ponit.</s> <s xml:id="echoid-s1276" xml:space="preserve"/> </p> <div xml:id="echoid-div42" type="float" level="2" n="2"> <figure xlink:label="fig-0110-01" xlink:href="fig-0110-01a"> <image file="0110-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0110-01"/> </figure> <figure xlink:label="fig-0111-01" xlink:href="fig-0111-01a"> <image file="0111-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0111-01"/> </figure> </div> <p> <s xml:id="echoid-s1277" xml:space="preserve">At quia plerumque paries, ſiue murus extrinſecus <lb/>(wntrc ſcarpc) ita latera obtegit, vt vix, ac ne vix quidem, <lb/>ab oppugnantibus vexari queant, ideo neceſſarium eſt, <lb/>parietes illos exſcindere, ac ita aperite, vt latera poſſint <lb/>oppugnati. </s> <s xml:id="echoid-s1278" xml:space="preserve">Implere foſſam & </s> <s xml:id="echoid-s1279" xml:space="preserve">eam cooperire, eſt res <lb/>valde longa & </s> <s xml:id="echoid-s1280" xml:space="preserve">difficilis, præcipuè ſi propugnantes ani-<lb/>mis & </s> <s xml:id="echoid-s1281" xml:space="preserve">vſu valeant. </s> <s xml:id="echoid-s1282" xml:space="preserve">Si munitio ſit terrea, ingredien-<lb/>dum eſt in foſſam, & </s> <s xml:id="echoid-s1283" xml:space="preserve">tentare an ligone conſumi poſſit, <lb/>vt ſæpe accidit. </s> <s xml:id="echoid-s1284" xml:space="preserve">Dicendũ jam eſt de cuniculis vel furnis: <lb/></s> <s xml:id="echoid-s1285" xml:space="preserve">maximos enim effectus gignunt, vt ſæpe docuit expe-<lb/>rientia, non ſolùm antiquis temporibus, ſed etiam ſæ-<lb/>culo noſtro. </s> <s xml:id="echoid-s1286" xml:space="preserve">Quòd ſi aliquando accidit non eum fru-<lb/>ctum tuliſſe, qui ab eis exſpectabatur, certum eſt hoc <lb/>accidiſſe, non ab ipſorum natura, ſed quòd perperam, <lb/>& </s> <s xml:id="echoid-s1287" xml:space="preserve">non vt decebat, ducti eſſent. </s> <s xml:id="echoid-s1288" xml:space="preserve">Hujus rei multæ cau-<lb/>ſæ poſſunt afferri. </s> <s xml:id="echoid-s1289" xml:space="preserve">Aliquando apparuit, dum cunicu-<lb/>lis muros vel aliquam munitionem terream ſubruere <lb/>conſtitutum erat, non fabricam illam ſubuerſam eſſe, <lb/>vt ſpes erat, ſed è contrà ignem erupiſſe in eam partem <lb/>oris quæ cenſebatur bene exſtructa & </s> <s xml:id="echoid-s1290" xml:space="preserve">clauſa, illacq́;</s> <s xml:id="echoid-s1291" xml:space="preserve"> <pb o="113" file="01130" n="138" rhead=""/> viam ſibi feciſſe. </s> <s xml:id="echoid-s1292" xml:space="preserve">Hujus euentus hæc eſſe potuit cauſa, <lb/>quòd ei furno vel cuniculo adeò parũ altitudinis tribu-<lb/>tum erat, vt puluis non potuerit ſuas vires exerere pro <lb/>ſolito ſuperiora petendo, ſed coactus ſit, ſeſe agglo-<lb/>merando, partem debiliorem petere, illacq́; </s> <s xml:id="echoid-s1293" xml:space="preserve">erumpere, <lb/>cum perexiguo fabricæ damno. </s> <s xml:id="echoid-s1294" xml:space="preserve">Ad hujuſce ſententiæ <lb/>confirmationem, afferam id quod vſu probatum eſt, <lb/>collocato ſcilicet puluere, non tamen in magna quan-<lb/>titate, in cellis aut aliis domiciliis, quæ non ita ab omni <lb/>parte occluſa erant, ſed varias aperturas habebant, ni-<lb/>mirum januas & </s> <s xml:id="echoid-s1295" xml:space="preserve">feneſtras, maximam nihilominus <lb/>ſtragem edidiſſe, immò multò majorem quàm ſpe-<lb/>ratum erat. </s> <s xml:id="echoid-s1296" xml:space="preserve">Non dubito, quin hoc acciderit, <lb/>quia ignis eam in altum diſtantiam habuit, vt fa-<lb/>cilè vires ſuas exerere potuerit, quæ tantæ fuerunt, <lb/>vt nulla moles oppoſita ſatis efficax fuerit ad eum re-<lb/>primendum, & </s> <s xml:id="echoid-s1297" xml:space="preserve">repellendum ad januas & </s> <s xml:id="echoid-s1298" xml:space="preserve">feneſtras, ſed <lb/>potiùs operatio facta fuerit pro natura illius elementi, <lb/>quod ſemper ſurſum tendit. </s> <s xml:id="echoid-s1299" xml:space="preserve">Quando igitur hi furni <lb/>& </s> <s xml:id="echoid-s1300" xml:space="preserve">cuniculi ducentur vt decet, eaq́; </s> <s xml:id="echoid-s1301" xml:space="preserve">forma, vt hoc ele-<lb/>mentum viribus ſuis vti poſſit, non dubium eſt quin <lb/>mirabiles effectus gignant. </s> <s xml:id="echoid-s1302" xml:space="preserve">Sed reuertamur ad id quod <lb/>coeperamus: </s> <s xml:id="echoid-s1303" xml:space="preserve">dirutis lateribus, & </s> <s xml:id="echoid-s1304" xml:space="preserve">explanata oppugna-<lb/>tione, ad aggreſſionem milites præparabuntur, benè <lb/>denſati, & </s> <s xml:id="echoid-s1305" xml:space="preserve">eo ordine, quem prudentiſſimus dux ju-<lb/>dicabit ex vſu eſſe. </s> <s xml:id="echoid-s1306" xml:space="preserve">Iam dicemus quomodo ſe <lb/>gerere debeant propugnatores, & </s> <s xml:id="echoid-s1307" xml:space="preserve">qui-<lb/>bus remediis judicamus <lb/>eos vti debere.</s> <s xml:id="echoid-s1308" xml:space="preserve"/> </p> <pb o="114" file="0114" n="139"/> <figure> <image file="0114-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0114-01"/> </figure> </div> <div xml:id="echoid-div44" type="section" level="1" n="36"> <head xml:id="echoid-head43" xml:space="preserve">Quo pacto ſe gerere debeant pro-<lb/>pugnatores, & quibus remediis <lb/>vti poſsint.</head> <head xml:id="echoid-head44" xml:space="preserve">CAPVT SEPTIMVM.</head> <p> <s xml:id="echoid-s1309" xml:space="preserve"><emph style="sc">QVvm</emph> dixerimus, quomodo ſe præpara-<lb/>re debeant ad expugnationem alicujus <lb/>ciuitatis ij qui obſident, dicemus jam de <lb/>ordine ac modo quem tenere debeant <lb/>ad ſui defenſionem oppugnati, & </s> <s xml:id="echoid-s1310" xml:space="preserve">de iis <lb/>quæ actu fieri debeant, tum ingenij, tum corporis vi-<lb/>ribus. </s> <s xml:id="echoid-s1311" xml:space="preserve">Et quia defenſio ciuitatis alicujus vel arcis, res <lb/>eſt tanti momenti, vt major reperiri non poſſit quæ <lb/>competat viro bellicoſo & </s> <s xml:id="echoid-s1312" xml:space="preserve">armis dedito, ajo talem vi-<lb/>rum audacem & </s> <s xml:id="echoid-s1313" xml:space="preserve">ſtrenuum eſſe debere, exercitatum, vi-<lb/>gilantiſſimum, & </s> <s xml:id="echoid-s1314" xml:space="preserve">qui conſiliis abundet, vt in quouis <lb/>repentino caſu remedia confidenter adhibeat, ſiue aga <lb/>tur de reparandis ruinis à tormentis hoſtilibus factis, ſi-<lb/>ue aliis quibuſuis quæ quotidie accidere poſſunt, vt <lb/>quum timor militum corda occupat, vel populus ita <lb/>vecors eſt, vt inde multa naſcantur incommoda. </s> <s xml:id="echoid-s1315" xml:space="preserve">O-<lb/>portet igitur vt cum prudentia, & </s> <s xml:id="echoid-s1316" xml:space="preserve">animi fortitudine, <lb/>timori obſiſtat & </s> <s xml:id="echoid-s1317" xml:space="preserve">ignorãtiæ reliquorum omnium:</s> <s xml:id="echoid-s1318" xml:space="preserve">tan-<lb/>tæq́; </s> <s xml:id="echoid-s1319" xml:space="preserve">majeſtatis & </s> <s xml:id="echoid-s1320" xml:space="preserve">grauitatis ſit, vt ipſius verba & </s> <s xml:id="echoid-s1321" xml:space="preserve">im-<lb/>peria omnes reuereantur & </s> <s xml:id="echoid-s1322" xml:space="preserve">pro bonis habeant. </s> <s xml:id="echoid-s1323" xml:space="preserve">At <lb/>hæc obtinere non poterit, niſi ſit vir magnæ experien-<lb/>tiæ, & </s> <s xml:id="echoid-s1324" xml:space="preserve">qui aliâs rationem honoratam ſuarum actio- <pb o="115" file="0115" n="140" rhead=""/> num reddiderit. </s> <s xml:id="echoid-s1325" xml:space="preserve">Præterea primus ſe operi accingat, <lb/>primus majora obeat pericula: </s> <s xml:id="echoid-s1326" xml:space="preserve">poſſit etiam ſua elo <lb/>quentia audaces ac ſtrenuos reliquos reddere. </s> <s xml:id="echoid-s1327" xml:space="preserve">Nam ſi <lb/>in magnis negotiis ac periculis, Præfectus arci in hunc <lb/>modum non ſe gerat, facillimè in ceſſet milites ſuos tr-<lb/>mor, quem vix, ac ne vix quidem, poſtea deponent. <lb/></s> <s xml:id="echoid-s1328" xml:space="preserve">Ea etiam indole ſit oportet, vt eum ſui facilè alloquan-<lb/>tur, audiatq́; </s> <s xml:id="echoid-s1329" xml:space="preserve">libenter monita & </s> <s xml:id="echoid-s1330" xml:space="preserve">delationes, quæ etiam <lb/>à priuatis militibus illi nunciantur, quia ſæpe ab iftis <lb/>ſana etiam conſilia prodeunt. </s> <s xml:id="echoid-s1331" xml:space="preserve">& </s> <s xml:id="echoid-s1332" xml:space="preserve">ſæpiſſimè apparuit in <lb/>infimæ ſortis homine recondita eſſe conſilia optima. </s> <s xml:id="echoid-s1333" xml:space="preserve"><lb/>Nolo tamen eum ſemper hæc conſilia ſequi, iisq́; </s> <s xml:id="echoid-s1334" xml:space="preserve">fi-<lb/>dem habere, ſcio enim ea non ſemper conducere: </s> <s xml:id="echoid-s1335" xml:space="preserve">ſed <lb/>volo Præfectum eligere id quod ex re ſua erit, reliqua <lb/>verò negligere. </s> <s xml:id="echoid-s1336" xml:space="preserve">Curet etiam ſumma cum dexteritate, <lb/>vt morem ſibi gerant: </s> <s xml:id="echoid-s1337" xml:space="preserve">non ſolùm milites, ſed etiam <lb/>incolæ loci. </s> <s xml:id="echoid-s1338" xml:space="preserve">Obedientia enim cenſetur inter præcipua <lb/>militiæ ornamẽta, & </s> <s xml:id="echoid-s1339" xml:space="preserve">ſine qua incaſſum reliqua omnia <lb/>fierent. </s> <s xml:id="echoid-s1340" xml:space="preserve">Sed quum non eadem indole præditæ ſint <lb/>omnes gentes, aliaq́; </s> <s xml:id="echoid-s1341" xml:space="preserve">ab alia mirum in modum variet, <lb/>opinor mitem animum & </s> <s xml:id="echoid-s1342" xml:space="preserve">manſuetum non ſemper <lb/>ex vſu eſſe, præcipuè erga milites, neque item ſeuerum <lb/>& </s> <s xml:id="echoid-s1343" xml:space="preserve">inexorabilem. </s> <s xml:id="echoid-s1344" xml:space="preserve">Vnde ex re erit, immò neceſſarium, <lb/>ſeueritatem cum manſuetudine miſcere, & </s> <s xml:id="echoid-s1345" xml:space="preserve">mores mu-<lb/>tare prout caſus feret, & </s> <s xml:id="echoid-s1346" xml:space="preserve">conditio ſtatus præſentis. </s> <s xml:id="echoid-s1347" xml:space="preserve">Con-<lb/>ſulo etiam huic noſtro Præfecto, vt prohibeat ſub gra-<lb/>uiſſima pœna, ne vllus ſuorum colloquia habeat cum <lb/>hoſte, vel etiam inter ſeſe de fœdere cum hoſte paci-<lb/>ſcendo. </s> <s xml:id="echoid-s1348" xml:space="preserve">Debetq́; </s> <s xml:id="echoid-s1349" xml:space="preserve">hunc rumorem ſumma diligentia <lb/>exſtinguere, vbi ſemel in vulgus ſerpere cœperit: </s> <s xml:id="echoid-s1350" xml:space="preserve">hæc <lb/>enim vſu veniunt in locis fere expugnatis, & </s> <s xml:id="echoid-s1351" xml:space="preserve">quæ in <pb o="116" file="0116" n="141" rhead=""/> magno periculo verſantur. </s> <s xml:id="echoid-s1352" xml:space="preserve">Quòd ſi hæc opinio vel <lb/>tantillas radices egerit, difficillimum erit impedire ne <lb/>milites rebellent, aliaq́; </s> <s xml:id="echoid-s1353" xml:space="preserve">id genus nimis periculoſa tra-<lb/>ctent. </s> <s xml:id="echoid-s1354" xml:space="preserve">Quum autem hoc conſilium particulare ſit, & </s> <s xml:id="echoid-s1355" xml:space="preserve"><lb/>maximi momenti ad conſeruationem nominis & </s> <s xml:id="echoid-s1356" xml:space="preserve">fa-<lb/>mæ noſtri Præfecti, in hoc debet is maximè prudens <lb/>& </s> <s xml:id="echoid-s1357" xml:space="preserve">attentus eſſe: </s> <s xml:id="echoid-s1358" xml:space="preserve">pluris enim eum faciet Princeps ſuus, <lb/>ſi ſe penitus perdiderit, forti & </s> <s xml:id="echoid-s1359" xml:space="preserve">inuicto animo prædi-<lb/>tus, quàm ſi ſe hoſti dedidiſſet, etiam ſi æquis & </s> <s xml:id="echoid-s1360" xml:space="preserve">ſibi <lb/>honorificis conditionibus id fieret: </s> <s xml:id="echoid-s1361" xml:space="preserve">quia in his non <lb/>ſita eſt plena Principis ſui ſatisfactio. </s> <s xml:id="echoid-s1362" xml:space="preserve">Sitamen à Prin-<lb/>cipe ſuper hac re mandata haberet, conſulo tunc vt <lb/>juſſis pareat, accipiatq́; </s> <s xml:id="echoid-s1363" xml:space="preserve">ab hoſte conditiones eas, quas <lb/>Princeps probauit. </s> <s xml:id="echoid-s1364" xml:space="preserve">Non debet autem rationem ha-<lb/>bere ſalutis & </s> <s xml:id="echoid-s1365" xml:space="preserve">voluntatis militum ſuorum. </s> <s xml:id="echoid-s1366" xml:space="preserve">Quia ſi Prę-<lb/>fectus aliquid patraret quod ſibi dedecori & </s> <s xml:id="echoid-s1367" xml:space="preserve">dehone-<lb/>ftamento eſſet, milites ob id non vituperarentur. </s> <s xml:id="echoid-s1368" xml:space="preserve">Præ-<lb/>fectus enim is eſt, in quem ſolum omnes oculos conji-<lb/>ciunt: </s> <s xml:id="echoid-s1369" xml:space="preserve">ei itaque ſoli competit rationem ſui & </s> <s xml:id="echoid-s1370" xml:space="preserve">ſuæ fa-<lb/>mæ reddere, tum coram Principe, tum etiam coram <lb/>omnibus. </s> <s xml:id="echoid-s1371" xml:space="preserve">Eſt autem res nimis moleſta Præfecto, vide-<lb/>re famam ſuam in dubium vocari, & </s> <s xml:id="echoid-s1372" xml:space="preserve">de ea homines <lb/>diſquirete. </s> <s xml:id="echoid-s1373" xml:space="preserve">Sed redeundo ad propugnationem & </s> <s xml:id="echoid-s1374" xml:space="preserve">de-<lb/>fenſionem noſtræ arcis, dico Præfectum quàm dili-<lb/>gentiſſimè, & </s> <s xml:id="echoid-s1375" xml:space="preserve">quantum fieri poterit, debere curare, vt <lb/>& </s> <s xml:id="echoid-s1376" xml:space="preserve">foſſa vacua ab omni impedimento maneat, & </s> <s xml:id="echoid-s1377" xml:space="preserve">via <lb/>quæ ad murum extrinſecum, quam omnes viam oper-<lb/>tam nominant: </s> <s xml:id="echoid-s1378" xml:space="preserve">alioquin hoſtis poſſet propiùs accede-<lb/>re: </s> <s xml:id="echoid-s1379" xml:space="preserve">hoc enim eſt magni momenti Præfecto, tum ad ſui <lb/>defenſionem, tum etiam vt hoſtem laceſſere poſſit, ne <lb/>facilè in foſſam ingrediatur, apertoq́; </s> <s xml:id="echoid-s1380" xml:space="preserve">muro extrinſe- <pb o="117" file="01170" n="142" rhead=""/> co, faciliùs tuas plateas inferiores (Galli caſcmatter) op-<lb/>pugnet, cuniculos agat, & </s> <s xml:id="echoid-s1381" xml:space="preserve">aggeres ligone ſubruat. </s> <s xml:id="echoid-s1382" xml:space="preserve">De-<lb/>bet etiam, vbi murus oppugnatur, ſæpe milites mitte-<lb/>re, qui foſſam inſpiciant ac recognoſcant, vt curet eam <lb/>purgari ruinis à tormentis factis. </s> <s xml:id="echoid-s1383" xml:space="preserve">Hæ enim ruinæ v-<lb/>ſum impediunt bombardarum quæ in feneſtris tor-<lb/>mentariis. </s> <s xml:id="echoid-s1384" xml:space="preserve">Quando autem vires hoſtium tantæ eſſent, <lb/>vt foſſarum tranſuerſarum ope, foſſæ tuæ vſu te priuaſ-<lb/>ſent, lateribus & </s> <s xml:id="echoid-s1385" xml:space="preserve">propugnationibus te nudaſſent, neceſſe <lb/>erit vt tantum te intrò retrahas, vt poſſis foſſas ducere, <lb/>quæ oppugnationem cingant: </s> <s xml:id="echoid-s1386" xml:space="preserve">quòd ſi tempus ad id <lb/>haberes, & </s> <s xml:id="echoid-s1387" xml:space="preserve">ſitus loci id concederet, nouos aggeres & </s> <s xml:id="echoid-s1388" xml:space="preserve"><lb/>nouas munitiones poſſes exſtruere, quales ſunt foſſæ <lb/>tranſuerſæ, propugnationes à latere, valla prominen-<lb/>tia, & </s> <s xml:id="echoid-s1389" xml:space="preserve">id genus alia, quæ poſſint oppugnationi & </s> <s xml:id="echoid-s1390" xml:space="preserve">ag-<lb/>greſſioni hoſtium reſiſtere. </s> <s xml:id="echoid-s1391" xml:space="preserve">Aduertendum eſt autem, <lb/>in caſu tam terrifico ac periculoſo, præcipuè vbi mu-<lb/>rus eſt dirutus, debere ſemper inſtructam tuorum <lb/>aciem habere in locis valdè propinquis ipſi oppugna <lb/>tioni, quorum primarij ſint loricati, idq́; </s> <s xml:id="echoid-s1392" xml:space="preserve">magno nu-<lb/>mero. </s> <s xml:id="echoid-s1393" xml:space="preserve">Et quia ſæpe accidit, vt quædam cataphracto-<lb/>rum turmæ, vel equitatus leuis, ſint in ciuitate ſeu arce <lb/>oppugnata, tales viri ita armati, ac equis relictis, mirum <lb/>in modum juuant in fronte aciei collocati, cum glo-<lb/>bo ſclopetariorum à latere foſſæ, (tranchcc,) qui trãſuer-<lb/>sè ejaculentur in labefactationem muri, (Gall. </s> <s xml:id="echoid-s1394" xml:space="preserve">bzcſchc.) <lb/></s> <s xml:id="echoid-s1395" xml:space="preserve">Debent autem eo ordine collocari milites circa foſſam <lb/>cum ſclopetariis, & </s> <s xml:id="echoid-s1396" xml:space="preserve">loricatis, qui haſtas prælongas ge-<lb/>rant (Galli piques armccs,) vt apparet in decimanona <lb/>& </s> <s xml:id="echoid-s1397" xml:space="preserve">vigeſima figuris.</s> <s xml:id="echoid-s1398" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1399" xml:space="preserve">Præterea ſæpe accidit, vt juxta muri labefactationem</s> </p> <pb o="118" file="0118" n="143" rhead=""/> <figure> <image file="0118-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0118-01"/> <caption xml:id="echoid-caption11" xml:space="preserve">DECIMAN@</caption> </figure> <pb file="0118_0119" n="144"/> <pb o="119" file="0119" n="145" rhead=""/> <figure> <image file="0119-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0119-01"/> <caption xml:id="echoid-caption12" xml:space="preserve">@A FIGVRA.</caption> </figure> <pb file="0120" n="146"/> <pb o="121" file="0121" n="147" rhead=""/> <figure> <image file="0121-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0121-01"/> </figure> <pb o="122" file="0122" n="148" rhead=""/> <figure> <image file="0122-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0122-01"/> <caption xml:id="echoid-caption13" xml:space="preserve">VICESIMA</caption> </figure> <pb file="0122_0123" n="149"/> <pb o="123" file="0123" n="150" rhead=""/> <figure> <image file="0123-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0123-01"/> <caption xml:id="echoid-caption14" xml:space="preserve">FIGVRA.</caption> </figure> <pb file="0124" n="151"/> <pb o="125" file="0125" n="152" rhead=""/> <p> <s xml:id="echoid-s1400" xml:space="preserve">domibus quibuſdam exiſtentibus, ab ipſa quidem op-<lb/>pugnatione majori ex parte apertis & </s> <s xml:id="echoid-s1401" xml:space="preserve">dirutis, muro-<lb/>rum tamen parte aliqua erecta adhuc manente, acci-<lb/>dit, inquam, vt illic collocati plures ſclopetarij, qui <lb/>tranſuersà in muri labefactationem jacularen-<lb/>tur, impedimento fuere quominus arx <lb/>ab hoſtibus expugnaretur, vt <lb/>viceſimaprima figura <lb/>apparet.</s> <s xml:id="echoid-s1402" xml:space="preserve"/> </p> <figure> <image file="0125-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0125-01"/> </figure> <pb o="126" file="0126" n="153" rhead=""/> <figure> <image file="0126-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0126-01"/> <caption xml:id="echoid-caption15" xml:space="preserve">VICESIMAPR</caption> </figure> <pb file="0126_0127" n="154"/> <pb o="127" file="0127" n="155" rhead=""/> <figure> <image file="0127-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0127-01"/> <caption xml:id="echoid-caption16" xml:space="preserve">@MA FIGVRA.</caption> </figure> <pb file="0128" n="156"/> <pb o="129" file="0129" n="157" rhead=""/> <p> <s xml:id="echoid-s1403" xml:space="preserve">Eſt igitur perneceſſarium vt præfectus arci valdè <lb/>ſit exercitatus, notitiamq́; </s> <s xml:id="echoid-s1404" xml:space="preserve">habeat omnium horum ca-<lb/>ſuum. </s> <s xml:id="echoid-s1405" xml:space="preserve">Sæpe etiam accidit, vt arcibus immineant mon-<lb/>tes, vel valla prominentia, (Galli cauafficrs,) quæ cor-<lb/>tinam directè oppugnent, ita vt vix, ac ne vix quidem, <lb/>tueri ſeſe poſſint obſeſſi: </s> <s xml:id="echoid-s1406" xml:space="preserve">præcipuè vbi arces ſunt adeò <lb/>paruæ, vt deſit ſpatium ad foſſas tranſuerſas ducendas. <lb/></s> <s xml:id="echoid-s1407" xml:space="preserve">Quòd ſi ſatis magnæ eſſent, ſpatiumq́; </s> <s xml:id="echoid-s1408" xml:space="preserve">ineſſet, poſſent <lb/>bonæfoſſæ tranſuerſæ duci, quarum ope oppu-<lb/>gnationi hoſtium obſiſteretur, vt vi-<lb/>ceſimaſecunda figura <lb/>apparet.</s> <s xml:id="echoid-s1409" xml:space="preserve"/> </p> <figure> <image file="0129-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0129-01"/> </figure> <pb o="130" file="0130" n="158" rhead=""/> <figure> <image file="0130-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0130-01"/> <caption xml:id="echoid-caption17" xml:space="preserve">VICESIMASE@</caption> </figure> <pb file="0130_0131" n="159"/> <pb o="131" file="0131" n="160" rhead=""/> <figure> <image file="0131-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0131-01"/> <caption xml:id="echoid-caption18" xml:space="preserve"><gap/>NDA FIGVRA.</caption> </figure> <pb o="132" file="0132" n="161" rhead=""/> <p> <s xml:id="echoid-s1410" xml:space="preserve">Quòd ſi forſan foſſæ tranſuerſæ duci non poſſent <lb/>ſuper aggere terreo, ob continuas oppugnationes ho-<lb/>ſtium è montibus & </s> <s xml:id="echoid-s1411" xml:space="preserve">vallis prominentibus, periculoſiſſi <lb/>mum tamen eſt, ſi hoſti relinquas ſummitatem aggeris <lb/>terrei, vel longiùs ab oppugnatione abſcedas: </s> <s xml:id="echoid-s1412" xml:space="preserve">ſed potes <lb/>te munire cum foſſis, à latere jaculari, & </s> <s xml:id="echoid-s1413" xml:space="preserve">locum ſtatio-<lb/>nis tuorum militum deprimere quantum poſſis. </s> <s xml:id="echoid-s1414" xml:space="preserve">Hoc <lb/>enim erit optimum remedium. </s> <s xml:id="echoid-s1415" xml:space="preserve">Non deſint tibi in hoc <lb/>periculo ignes artificiales omnigeni, cornua, pilæ, <lb/>mala punica, & </s> <s xml:id="echoid-s1416" xml:space="preserve">ſimilia. </s> <s xml:id="echoid-s1417" xml:space="preserve">Præteiea mirum in modum <lb/>impediunt hoſtes, ſi murices in ſolum ſpargantur, vel <lb/>tabulæ, quibus frequentes claui ſint infixi. </s> <s xml:id="echoid-s1418" xml:space="preserve">Quòd ſi <lb/>hæc omnia deſint, vel, ſi nihil profuerint, collocanda <lb/>erit magna ſtrues lignorum in introitu, &</s> <s xml:id="echoid-s1419" xml:space="preserve">, vbi hoſtis <lb/>ſuperuenerit, ignis injiciendus. </s> <s xml:id="echoid-s1420" xml:space="preserve">Hocce tibi <lb/>aliquantulum temporis impertiet, <lb/>quo poſſis tuis rebus <lb/>conſulere.</s> <s xml:id="echoid-s1421" xml:space="preserve"/> </p> <figure> <image file="0132-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0132-01"/> </figure> <pb o="133" file="0133" n="162"/> <figure> <image file="0133-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0133-01"/> </figure> </div> <div xml:id="echoid-div45" type="section" level="1" n="37"> <head xml:id="echoid-head45" xml:space="preserve">Exercitus, ſiue aciei, itinera, caſtro-<lb/>rum metationes, & quomodo eæ <lb/>metationes fieri debeant.</head> <head xml:id="echoid-head46" xml:space="preserve">CAPVT OCTAVVM.</head> <p> <s xml:id="echoid-s1422" xml:space="preserve"><emph style="sc">HVcvsqve</emph> dictum eſt de variis generi-<lb/>bus munitionum, de conſeruatione ac <lb/>defenſione, necnon & </s> <s xml:id="echoid-s1423" xml:space="preserve">de expugnatione <lb/>ipſarum, idq́; </s> <s xml:id="echoid-s1424" xml:space="preserve">quantum fieri potuit bre-<lb/>uiſſimè, de iis tantummodo agens, quæ <lb/>magis neceſſaria mihi viſa ſunt ad militem noſtrum <lb/>doctrina militari informandum. </s> <s xml:id="echoid-s1425" xml:space="preserve">Dicam jam de itine-<lb/>ribus, de caſtrorum metationibus & </s> <s xml:id="echoid-s1426" xml:space="preserve">ſtationibus. </s> <s xml:id="echoid-s1427" xml:space="preserve">(Gal. <lb/></s> <s xml:id="echoid-s1428" xml:space="preserve">fogie.)</s> <s xml:id="echoid-s1429" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1430" xml:space="preserve">Quando exercitus progreditur, habens proximum <lb/>ſibi exercitum hoſtilem, multa debet perpendere is qui <lb/>ei præeſt. </s> <s xml:id="echoid-s1431" xml:space="preserve">Primò ſi viribus inferior ſit exercitu hoſtili, <lb/>ob idq́; </s> <s xml:id="echoid-s1432" xml:space="preserve">nolit manus cum hoſte conferre, ne fortunæ <lb/>vnius diei cõmittat quicquid habet ac poſſidet, debet <lb/>incedere per colles & </s> <s xml:id="echoid-s1433" xml:space="preserve">loca montoſa, & </s> <s xml:id="echoid-s1434" xml:space="preserve">rebus ſuis ita <lb/>proſpicere, vt ſemper ſit in munitiori ac commodiori <lb/>loco, ſic vt hoſtis, ſi prudens ſit, non audeat eum ag-<lb/>gredi. </s> <s xml:id="echoid-s1435" xml:space="preserve">Vbi tamen prælium effugere non poterit, de-<lb/>bet curare vt id committat cum majori ſuo emolu-<lb/>mento, immò cum certa victoriæ ſpe: </s> <s xml:id="echoid-s1436" xml:space="preserve">quod illi diffi-<lb/>cile non erit, ſi ſaltem ſciat ex ſitus commoditate quæ- <pb o="134" file="0134" n="163" rhead=""/> ſtum facere. </s> <s xml:id="echoid-s1437" xml:space="preserve">Dum progreditur, conſulo vt partem <lb/>equitum leuis armaturæ ita vicinam exercitui hoſtili <lb/>habeat, vt ſingulis momentis certior fiat de itinere, ac <lb/>reliquo omni ſtatu hoſtium. </s> <s xml:id="echoid-s1438" xml:space="preserve">Certum autem eſt, quan-<lb/>do regio plana ſit, ſine montibus, ſine collibus, immi-<lb/>neatq́; </s> <s xml:id="echoid-s1439" xml:space="preserve">hoſtis, vix, ac ne vix quidem, poſſe tũc prælium <lb/>effugi: </s> <s xml:id="echoid-s1440" xml:space="preserve">tunc igitur non abnuerem, immò conſulerem <lb/>vt prælium committeret, modò longè ſuperior ſit e-<lb/>quitatu: </s> <s xml:id="echoid-s1441" xml:space="preserve">equitatus enim, in locis patentibus, vt pluri-<lb/>mum victoriam ſuis tribuit, modò eo bene & </s> <s xml:id="echoid-s1442" xml:space="preserve">com-<lb/>modè vtamur. </s> <s xml:id="echoid-s1443" xml:space="preserve">Hanc rationem ſequuti ſunt antiqui: </s> <s xml:id="echoid-s1444" xml:space="preserve">in-<lb/>ter quos Fabius Maximus, quando tamdiu cum acie <lb/>Romana caſtrametabatur prope victorem Annibalẽ. <lb/></s> <s xml:id="echoid-s1445" xml:space="preserve">Et noſtris temporibus, in Germania Carolus Quintus <lb/>Imperator exercitum ducens aduerſus Proteſtantes, <lb/>vix tandem potuit eos ad prælium cogere, propter <lb/>commoditatem locorum montoſorum & </s> <s xml:id="echoid-s1446" xml:space="preserve">collibus re-<lb/>fertorũ, per quæ ij exercitum ſuum ductabant, idq́; </s> <s xml:id="echoid-s1447" xml:space="preserve">tam <lb/>prope Imperatorem, vt non plus ab eo diſtarent, quàm <lb/>quò pertingere poſſet ejaculatio bombàrdæ. </s> <s xml:id="echoid-s1448" xml:space="preserve">Sed <lb/>rarò hoc accidit in locis patentibus. </s> <s xml:id="echoid-s1449" xml:space="preserve">In his, qui confli-<lb/>ctum abnuit, debet ab hoſte abeſſe octo aut decem <lb/>miliaribus Italicis ad minus: </s> <s xml:id="echoid-s1450" xml:space="preserve">munireq́; </s> <s xml:id="echoid-s1451" xml:space="preserve">ita ſedes ac <lb/>ſtationes ſuas, vt nec equitatus, nec ipſi pedites, poſ-<lb/>ſint in ſua caſtra irrumpere, niſi cum ſumma difficulta-<lb/>te. </s> <s xml:id="echoid-s1452" xml:space="preserve">Hocq́; </s> <s xml:id="echoid-s1453" xml:space="preserve">ſatis ſit pro munitione campeſtri, quæ ci-<lb/>tò ac raptim fieri debet, vbi exercitus cogitur in plani-<lb/>tie ſtare per aliquot horas aut dies. </s> <s xml:id="echoid-s1454" xml:space="preserve">Quòd ſi diutiùs a-<lb/>licubi ſtare voluerit, poterit caſtra ſua munire prout ex <lb/>vſu eſſe judicabit. </s> <s xml:id="echoid-s1455" xml:space="preserve">Quum progreditur exercitus per pla <lb/>nities & </s> <s xml:id="echoid-s1456" xml:space="preserve">loca patentia, curet dux ipſius, quando ita fie- <pb o="135" file="0135" n="164" rhead=""/> ri poſſit, vt fluuius vel riuus aliquis, ſeu ſylua operiat la-<lb/>tus vnum aciei ſuæ: </s> <s xml:id="echoid-s1457" xml:space="preserve">hæc enim commoditas illi erit ma-<lb/>ximo emolumento. </s> <s xml:id="echoid-s1458" xml:space="preserve">Videat etiam vt impedimenta & </s> <s xml:id="echoid-s1459" xml:space="preserve"><lb/>bombardæ ab ea parte ducantur quæ non hoſtem ſpe-<lb/>ctat. </s> <s xml:id="echoid-s1460" xml:space="preserve">In parte autem quæ ad hoſtem vergit, collocet <lb/>ordine decenti cataphractorum turmas, quæ latus pe-<lb/>ditum muniant & </s> <s xml:id="echoid-s1461" xml:space="preserve">ipſum medium exercitum. </s> <s xml:id="echoid-s1462" xml:space="preserve">Lauda-<lb/>tur hæc conſuetudo, quæ vniuerſam aciem in tres glo-<lb/>bos diuidit. </s> <s xml:id="echoid-s1463" xml:space="preserve">Priores ſcilicet, qui à Gallis auantgardc, me-<lb/>dios, qui bataiſſe, poſteriores, qui arriezcgardc. </s> <s xml:id="echoid-s1464" xml:space="preserve">Debent <lb/>autem ſingulis diebus hi tres globi vices mutare, ita <lb/>vt primi ſint medij, & </s> <s xml:id="echoid-s1465" xml:space="preserve">medij poſtremi, & </s> <s xml:id="echoid-s1466" xml:space="preserve">poſtremi pri-<lb/>mi, vel alio modo: </s> <s xml:id="echoid-s1467" xml:space="preserve">confleturq́; </s> <s xml:id="echoid-s1468" xml:space="preserve">vnuſquiſque horum <lb/>globorum ex numero competenti militum, tum equi-<lb/>tum, tum ſclopetariorum. </s> <s xml:id="echoid-s1469" xml:space="preserve">Præterea magna eſt adhi-<lb/>benda cura, ne inter peditum cohortes immiſceantur <lb/>lixæ & </s> <s xml:id="echoid-s1470" xml:space="preserve">id genus hominum nihili: </s> <s xml:id="echoid-s1471" xml:space="preserve">ſtentq́; </s> <s xml:id="echoid-s1472" xml:space="preserve">omnes mili-<lb/>tes in loco aſſignato, vnuſquiſque ſub ſuo vexillo. </s> <s xml:id="echoid-s1473" xml:space="preserve">Sint <lb/>item omnes equeſtres turmæ vacuæ ab equis inutili-<lb/>bus, & </s> <s xml:id="echoid-s1474" xml:space="preserve">ab omnibus aliis impedimentis. </s> <s xml:id="echoid-s1475" xml:space="preserve">Laudandi ſunt <lb/>equites Germani, qui ſumma diligentia vtuntur, præ-<lb/>cipuè in ordine ſeruando, in quo mirum in modum <lb/>ſunt exacti:</s> <s xml:id="echoid-s1476" xml:space="preserve">ideoq́; </s> <s xml:id="echoid-s1477" xml:space="preserve">magna laus illis debetur. </s> <s xml:id="echoid-s1478" xml:space="preserve">Probatur <lb/>etiam hic mos, vt equitatus leuis ita diſponatur, vt re-<lb/>gionem luſtret ac recognoſcat, inſpectorq́; </s> <s xml:id="echoid-s1479" xml:space="preserve">diligens ſit <lb/>omnium eorum, quæ ab hoſtili exercitu fiunt, vt ſin-<lb/>gulis momẽtis de iis certiorem faciat ducem ſuum, vt, <lb/>ſi vſu veniat, tempus & </s> <s xml:id="echoid-s1480" xml:space="preserve">commoditatem habeat ad præ-<lb/>lium ſe præparandi. </s> <s xml:id="echoid-s1481" xml:space="preserve">De itinere exercitus, ſpecialis ca-<lb/>non dari non poteſt, quia pro natura ſitus, ac quali-<lb/>tate regionis, iter accommodatur. </s> <s xml:id="echoid-s1482" xml:space="preserve">Tranſibimus <pb o="136" file="0136" n="165" rhead=""/> igitur ad caſtrametationem, dicemusq́; </s> <s xml:id="echoid-s1483" xml:space="preserve">de ſitu, forma, <lb/>magnitudine, munitione, cõmoditate, & </s> <s xml:id="echoid-s1484" xml:space="preserve">ordine ipſius, <lb/>prout ex vſu erit. </s> <s xml:id="echoid-s1485" xml:space="preserve">Quòd ad ſitum attinet, dico, ſi caſtra <lb/>ſint in planitie, longè à collibus, neceſſariò debent <lb/>juxta ſe habere vel flumen, vel alias laudabiles aquas, <lb/>quæ commodè poſſint exercitum alere, necnon & </s> <s xml:id="echoid-s1486" xml:space="preserve">e-<lb/>quos: </s> <s xml:id="echoid-s1487" xml:space="preserve">debet etiam curari vt in proximo ſit lignatio ad <lb/>neceſſarios vſus exercitus. </s> <s xml:id="echoid-s1488" xml:space="preserve">Pabulum item ſit in vicinia <lb/>pro equis & </s> <s xml:id="echoid-s1489" xml:space="preserve">jumentis. </s> <s xml:id="echoid-s1490" xml:space="preserve">Hæc enim non poteſt ſecum <lb/>deferre exercitus. </s> <s xml:id="echoid-s1491" xml:space="preserve">Quum hi commeatus in caſtra <lb/>erunt deportati, debent caſtra ita muniri vt hoſtis non <lb/>poſſit eos ſubripere. </s> <s xml:id="echoid-s1492" xml:space="preserve">Magnitudo & </s> <s xml:id="echoid-s1493" xml:space="preserve">circumferentia <lb/>metationis non debet eſſe tam vaſta, vt non poſſint <lb/>facilè & </s> <s xml:id="echoid-s1494" xml:space="preserve">in promptu alij aliis ſuppetias ferre, vbi vſu <lb/>veniat, ſeſeq́; </s> <s xml:id="echoid-s1495" xml:space="preserve">inuicem tueri. </s> <s xml:id="echoid-s1496" xml:space="preserve">Neque ſit ita exigua, vt <lb/>exercitus priuetur omnibus ſuis commoditatibus, & </s> <s xml:id="echoid-s1497" xml:space="preserve"><lb/>plateis neceſſariis, vel pro acie inſtruenda, pro foro, <lb/>pro mercatoribus qui caſtra ſequuntur, & </s> <s xml:id="echoid-s1498" xml:space="preserve">aliis id ge-<lb/>nus. </s> <s xml:id="echoid-s1499" xml:space="preserve">Forma erit ea quæ à nobis deſcripta eſt, habita <lb/>tamen ſitus ratione. </s> <s xml:id="echoid-s1500" xml:space="preserve">In noſtra deſcriptione diſtinctæ <lb/>ſunt omnes regiones cum ſuis plateis, viæ per quas <lb/>exitur, & </s> <s xml:id="echoid-s1501" xml:space="preserve">Imperatoris tabernaculum: </s> <s xml:id="echoid-s1502" xml:space="preserve">quæ omnia ſum-<lb/>ma facilitate declarantur. </s> <s xml:id="echoid-s1503" xml:space="preserve">Si accidat metati onem fieri <lb/>in loco montoſo, collibus referto, variè compoſito, <lb/>vallibus, præcipitiis, fluuiis, ſyluis, cauernis, & </s> <s xml:id="echoid-s1504" xml:space="preserve">aliis id <lb/>genus:</s> <s xml:id="echoid-s1505" xml:space="preserve">modò arte militari valeat noſter Imperator, ſitq́; <lb/></s> <s xml:id="echoid-s1506" xml:space="preserve">caſtrametandi peritus, magno adjumento illi erit talis <lb/>ſitus, ac cum minimo labore & </s> <s xml:id="echoid-s1507" xml:space="preserve">arte caſtra ſua fortiſſi-<lb/>mè muniet. </s> <s xml:id="echoid-s1508" xml:space="preserve">Sed in primis cauere debet, ne metetur <lb/>in loco, cui immineant colles vel juga, ex quibus fa-<lb/>cilè poſſint introſpici caſtra, & </s> <s xml:id="echoid-s1509" xml:space="preserve">cortinæ aggerum op- <pb o="137" file="0137" n="166" rhead=""/> pugnari. </s> <s xml:id="echoid-s1510" xml:space="preserve">Ita enim vexatus ab hoſtili exercitu, cogere-<lb/>tur ſedes mutare, vel etiam prælium committere maxi-<lb/>mo ſuo incommodo, ſicut fere accidit Franciſco Gal-<lb/>liarum Regi dum ſederet ad Cambreſium. </s> <s xml:id="echoid-s1511" xml:space="preserve">Relicto <lb/>enim ab vna parte ſuorum caſtrorum colle, è quo ad-<lb/>notari poterat quidquid erat in ſuis caſtris, & </s> <s xml:id="echoid-s1512" xml:space="preserve">cortina <lb/>ipſorum oppugnari, quum appuliſſet Carolus quin-<lb/>tus Imperator cum ſuo exercitu, isq́; </s> <s xml:id="echoid-s1513" xml:space="preserve">locus à ſuis lega-<lb/>tis fuiſſet animaduerſus, conſilium Imperatori datum <lb/>eſt, vt quamuis diei parum ſupereſſet, & </s> <s xml:id="echoid-s1514" xml:space="preserve">exercitus fati-<lb/>gatus ob laborem ac moleſtiam illius diei, nihilomi-<lb/>nus occaſionem arriperet, & </s> <s xml:id="echoid-s1515" xml:space="preserve">locum illum occuparet <lb/>mirum in modum ſibi commodum. </s> <s xml:id="echoid-s1516" xml:space="preserve">Verùm huic pru-<lb/>dentiſſimo ac vtiliſſimo cõſilio quidã magnæ auctori-<lb/>tatis viri ſeſe oppoſuerunt, dicentes hoc niſi cum maxi <lb/>ma & </s> <s xml:id="echoid-s1517" xml:space="preserve">aperta difficultate eo temporis momẽto exequi <lb/>nõ potuiſſe, ſibi autem liberũ eſſe ſummo ſequenti ma-<lb/>ne, loco illo potiri. </s> <s xml:id="echoid-s1518" xml:space="preserve">Quod tamen non ſucceſſit. </s> <s xml:id="echoid-s1519" xml:space="preserve">Quum <lb/>enim Chriſtianiſſimus Rex erratum ſuum agnouiſſet, <lb/>eadem nocte miſit eò pedites Italos, qui locum illum <lb/>occuparent ac munirent. </s> <s xml:id="echoid-s1520" xml:space="preserve">Vt autem faciliùs hæc caſtro-<lb/>rum metatio innoteſcat, illius exemplum dabimus cum <lb/>ſua figura.</s> <s xml:id="echoid-s1521" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1522" xml:space="preserve">Vt aptè fiant metationes in loco plano, cum ſuis <lb/>menſuris, ad ſitum accommodatis, neceſſariò ſcien-<lb/>dum eſt quæ ſint ſuperficies regionum equitatus & </s> <s xml:id="echoid-s1523" xml:space="preserve">pe-<lb/>ditatus, cum ſuis plateis, viis, & </s> <s xml:id="echoid-s1524" xml:space="preserve">aliis rebus ad caſtro-<lb/>rum vſum neceſſariis. </s> <s xml:id="echoid-s1525" xml:space="preserve">Exempli gratia, ſtatuamus exer-<lb/>citum habere 60000 militum, in quibus 2000 cata-<lb/>phracti, 10000 leuis equitatus, & </s> <s xml:id="echoid-s1526" xml:space="preserve">48000 tum ſclopeta-<lb/>riorum, tum haſtatorum loricatorum, (pigucs armcce,) <pb o="138" file="0138" n="167" rhead=""/> tum haſtatorum inermium, (piqucs ſcichce.) </s> <s xml:id="echoid-s1527" xml:space="preserve">Vnicuique <lb/>cataphracto ſeptem ſpatia aſſignabimus: </s> <s xml:id="echoid-s1528" xml:space="preserve">equiti verò le-<lb/>uis armaturæ quatuor. </s> <s xml:id="echoid-s1529" xml:space="preserve">Vnumquodque autem ſpa-<lb/>tium erit 50 pedum terræ ſuperficialium, 5 ſcilicet in <lb/>latitu dinem, 10 verò in longitudinem.</s> <s xml:id="echoid-s1530" xml:space="preserve"/> </p> <figure> <image file="0138-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0138-01"/> </figure> <p> <s xml:id="echoid-s1531" xml:space="preserve">Vnicuique pediti cum ſuo famulo dabuntur terræ <lb/>64 pedes ſuperficiales, 8 videlicet pedes quaquauer-<lb/>ſum, vt hac figura apparet.</s> <s xml:id="echoid-s1532" xml:space="preserve"/> </p> <figure> <image file="0138-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0138-02"/> </figure> <p> <s xml:id="echoid-s1533" xml:space="preserve">Hoc facto deſignabitur Imperatoris platea, quadra-<lb/>ginta vel quinquaginta paſſuum quadratorum in ipſo <lb/>caſtrorum meditullio. </s> <s xml:id="echoid-s1534" xml:space="preserve">Ducentur deinde duæ viæ, quæ <pb o="139" file="0139" n="168" rhead=""/> ſe ad angulos rectos ſecent in medio plateæ Imperato-<lb/>ris, viæ præcipuæ nuncupatæ, quarum capita ſtationes <lb/>præſidiariæ erunt hoſtem verſus. </s> <s xml:id="echoid-s1535" xml:space="preserve">Circa Imperatoris <lb/>plateam collocemus 500 milites ſtrenuos (appoinctés) <lb/>quorum vnicuiq, duo ſpatia dabimus ejuſdem ſuper-<lb/>ficiei qua erant ſpatia tributa equitibus, tum cataphra-<lb/>ctis, tum etiam leuis armaturæ. </s> <s xml:id="echoid-s1536" xml:space="preserve">Præterea, circa Impe-<lb/>ratoris plateam deſignabimus duas alias plateas, hanc <lb/>pro mercatu, illam verò pro macello, tributo amba-<lb/>bus eodem terræ ſpatio, quod quingentis ſtrenuis de-<lb/>putatum eſt. </s> <s xml:id="echoid-s1537" xml:space="preserve">Circum haſce plateas, & </s> <s xml:id="echoid-s1538" xml:space="preserve">ſtrenuorum ſe-<lb/>dem, deſignabimus viam quinque paſſuum, circa <lb/>quam locabimus regiones cataphractorum & </s> <s xml:id="echoid-s1539" xml:space="preserve">leuis <lb/>equitatus, cum ſuis viis & </s> <s xml:id="echoid-s1540" xml:space="preserve">plateis in medio. </s> <s xml:id="echoid-s1541" xml:space="preserve">Circa re-<lb/>giones equitum deſcribetur via decem paſſuum in lati-<lb/>tudine, & </s> <s xml:id="echoid-s1542" xml:space="preserve">circa hanc viam regiones peditum, cum <lb/>ſuis viis & </s> <s xml:id="echoid-s1543" xml:space="preserve">plateis. </s> <s xml:id="echoid-s1544" xml:space="preserve">In capite autem viæ quæ ad hoſtem <lb/>vergit, platea generalis armorum deſignabitur, quæ in <lb/>ſuperficie habebit dimidium ejus ſpatij quod pediti-<lb/>bus tributum eſt: </s> <s xml:id="echoid-s1545" xml:space="preserve">licet hæc platea in noſtra ichnogra-<lb/>phia non ſit vbiq; </s> <s xml:id="echoid-s1546" xml:space="preserve">ea amplitudine delineata, quia foſſa <lb/>tam longè à caſtris diſtat, vt inter eam & </s> <s xml:id="echoid-s1547" xml:space="preserve">caſtra facile <lb/>ſit plateam armorum eligere. </s> <s xml:id="echoid-s1548" xml:space="preserve">In extremitate, quæ ad <lb/>hoſtem vergit, deſignabitur platea ad commeatum <lb/>bombardicum. </s> <s xml:id="echoid-s1549" xml:space="preserve">Et in calce vel humero caſtrorum lo-<lb/>cabuntur foſſores (pionnicze,) cum pecoribus quæ ad <lb/>exercitus victũ mactantur, & </s> <s xml:id="echoid-s1550" xml:space="preserve">aliis rebus parui momẽti. <lb/></s> <s xml:id="echoid-s1551" xml:space="preserve">Annonæ ſtructores, macellarij, cupedinarij, diuidentur <lb/>per plateas regionum, & </s> <s xml:id="echoid-s1552" xml:space="preserve">ad oram viarum. </s> <s xml:id="echoid-s1553" xml:space="preserve">Foſſæ à <lb/>caſtris diſtabunt 40 aut 50 paſſibus. </s> <s xml:id="echoid-s1554" xml:space="preserve">Quomodo autem <lb/>hæc omnia deſignari debeant, exemplis palàm facie- <pb o="140" file="0140" n="169" rhead=""/> mus. </s> <s xml:id="echoid-s1555" xml:space="preserve">Primò deſignabitur platea Imperatoris in ipſo <lb/>meditullio caſtrorum, vt ſuprà dictum eſt. </s> <s xml:id="echoid-s1556" xml:space="preserve">Statuamus <lb/>autem eam habere in ſuperficie quaquauerſum 50 paſ-<lb/>ſus. </s> <s xml:id="echoid-s1557" xml:space="preserve">Ducemus deinde duas vias, quas diximus ſeſe in-<lb/>terſecare ad angulos rectos in ipſo meditullio plateæ <lb/>Imperatoris. </s> <s xml:id="echoid-s1558" xml:space="preserve">Habebuntq́; </s> <s xml:id="echoid-s1559" xml:space="preserve">15 paſſus in latitudine. </s> <s xml:id="echoid-s1560" xml:space="preserve">Poſt <lb/>hæc ſedem dabimus 500 ſtrenuis viris circum mediam <lb/>partem plateæ Imperatoris quæ ad hoſtem vergit. </s> <s xml:id="echoid-s1561" xml:space="preserve">Vt <lb/>id fiat, ſubtrahemus pro latitudine viarum 15 paſſus à <lb/>50, remanebunt 35: </s> <s xml:id="echoid-s1562" xml:space="preserve">& </s> <s xml:id="echoid-s1563" xml:space="preserve">à 35 dimidium auferemus, quod <lb/>erit 17 cum dimidio. </s> <s xml:id="echoid-s1564" xml:space="preserve">Hæc autem 17 cum dimidio in <lb/>ſe ducemus, prodibunt paſſus ſuperficiales 306. </s> <s xml:id="echoid-s1565" xml:space="preserve">Dein-<lb/>de ſumemus dimidium 500 virorum ſtrenuorum, vt <lb/>ab vtraque parte viæ ad plateæ oram ſedeant illo-<lb/>rum 250. </s> <s xml:id="echoid-s1566" xml:space="preserve">Iam ducam 250 in 100, (ſuperficiem ſcilicet <lb/>duorum ſpatiorum equitibus aſſignatorum,) prodi-<lb/>bunt pedes ſuperficiales 25000. </s> <s xml:id="echoid-s1567" xml:space="preserve">quos 25000 diuidemus <lb/>per 25 pedes ſuperficiales, hos pedes in paſſus reducen-<lb/>do (quilibet enim paſſus æquipollet 25 pedibus ſuper-<lb/>ficialibus) pro dibunt paſſus 1000: </s> <s xml:id="echoid-s1568" xml:space="preserve">quibus 1000 paſ-<lb/>ſibus addemus paſſus ſuperficiales 306, quos ſuprà ha-<lb/>bebamus, prodibunt paſſus 1306, à quibus radicem <lb/>quadratam extrahemus, quæ erit circa 36. </s> <s xml:id="echoid-s1569" xml:space="preserve">A 36 aufe-<lb/>remus 17 cum dimidio: </s> <s xml:id="echoid-s1570" xml:space="preserve">ſuperſunt 18 cum dimidio: </s> <s xml:id="echoid-s1571" xml:space="preserve">qui <lb/>paſſus 18 cum dimidio dimetientur ad oram viarum, <lb/>initium ſumendo ab Imperatoris platea. </s> <s xml:id="echoid-s1572" xml:space="preserve">& </s> <s xml:id="echoid-s1573" xml:space="preserve">ab extremi-<lb/>tate 18 cum dimidio ducẽtur lineæ ad angulos rectos, <lb/>deſignabunturq́; </s> <s xml:id="echoid-s1574" xml:space="preserve">ſedes pro nobilibus, ſeu viris ſtrenuis, <lb/>vt in ichnographia noſtra apparet. </s> <s xml:id="echoid-s1575" xml:space="preserve">Ab alia verò parte <lb/>plateæ Imperatoris, formabuntur duæ plateæ, hæc pro <lb/>macello, illa verò pro mercatu, ejuſdem capacitatis, <pb o="141" file="0141" n="170" rhead=""/> qua ſunt loca virorum ſtrenuorum. </s> <s xml:id="echoid-s1576" xml:space="preserve">Circum verò <lb/>ſedes virorum ſtrenuorum, & </s> <s xml:id="echoid-s1577" xml:space="preserve">circum plateas, deſi-<lb/>gnabimus viam latitudine quinque paſſuum, ac cir-<lb/>cum eam regiones cataphractorum & </s> <s xml:id="echoid-s1578" xml:space="preserve">equitatus leuis, <lb/>cum ſuis viis & </s> <s xml:id="echoid-s1579" xml:space="preserve">plateis armorum hoc modo. </s> <s xml:id="echoid-s1580" xml:space="preserve">Primò <lb/>multiplicabimus ſeptem ſpatia, quæ vnicuique cata-<lb/>phracto dantur, quæq́; </s> <s xml:id="echoid-s1581" xml:space="preserve">continent pedes ſuperficiales <lb/>350, per 2000, (totenim ſunt cataphracti,) prodibunt <lb/>pedes ſuperficiales 700000, quibus in paſſus reductis, & </s> <s xml:id="echoid-s1582" xml:space="preserve"><lb/>per 25 diuiſis, prodibũt paſſus ſuperficiales 28000 pro <lb/>cataphractis. </s> <s xml:id="echoid-s1583" xml:space="preserve">Deinde dabitur illis ſua arm orum platea, <lb/>cum duobus locis cataphracti, quæ ſunt pedes 100 <lb/>ſuperficiales. </s> <s xml:id="echoid-s1584" xml:space="preserve">Multiplico 2000 cum 100, prodeunt <lb/>200000, quæ diuido per 25, fiunt 8000 paſſus ſuperfi-<lb/>ciales, quibus additis ad 28000, qui ſuprà, fient 36000 <lb/>paſſus ſuperficiales pro ſedibus cataphractorum cum <lb/>ſua armorum platea. </s> <s xml:id="echoid-s1585" xml:space="preserve">Idq́; </s> <s xml:id="echoid-s1586" xml:space="preserve">ſpatium cataphractis com-<lb/>petit. </s> <s xml:id="echoid-s1587" xml:space="preserve">Hoc facto videndum, quale ſpatium competit <lb/>equitatui leuis armaturæ cum ſuis armorum plateis. <lb/></s> <s xml:id="echoid-s1588" xml:space="preserve">Multiplicando 10000 (tot ſunt equites leuis armaturę) <lb/>cum quatuor ſpatiis quæ vnicuique dantur, quæ ſpatia <lb/>continentpedes ſuperficiales 200, prodibunt 2000000, <lb/>quibus per 25 diuiſis, remanebunt paſſus ſuperficiales <lb/>80000. </s> <s xml:id="echoid-s1589" xml:space="preserve">Deinde iſtis dabimus ſuam armorum pla-<lb/>team, cum ſpatio vnius equitis leuis armaturæ, mul-<lb/>tiplicando 50 per 10000, prodibunt 500000, quibus <lb/>per 25 diuiſis, prodibunt paſſus ſuperficiales 20000, <lb/>qui additi ad 80000, facient 100000. </s> <s xml:id="echoid-s1590" xml:space="preserve">Tot igitur pe-<lb/>des ſuperficiales tribuentur equitatui leuis armaturæ <lb/>cum ſuis armorum plateis. </s> <s xml:id="echoid-s1591" xml:space="preserve">Iam hoſce 100000 paſſus <lb/>addemus ad 36000, (ſpatium ſcilicet cataphractis de- <pb o="142" file="0142" n="171" rhead=""/> bitum,) fient 136000, quibus per 4 diuiſis, (in qua-<lb/>tuor enim regiones diſtribuendi ſunt tum cataphracti, <lb/>tum equites leuis armaturæ) prodibũt 34000 pro vna-<lb/>quaque regione, non comprehenſis ſuis viis, quæ re-<lb/>ctà tendunt ad ſuas armorum plateas, vt ex noſtra <lb/>ichnographia apparet. </s> <s xml:id="echoid-s1592" xml:space="preserve">Quas vias vt cum his qua-<lb/>tuor regionibus comprehendamus, extrahemus radi-<lb/>cem quadratam à 34000, quæ erit paulo plus quàm <lb/>184: </s> <s xml:id="echoid-s1593" xml:space="preserve">quibus 184 addemus paſſus decem pro viarum <lb/>latitudine, fient 194, quæ 194 rurſum in ſe ducemus, <lb/>prodibuntq́; </s> <s xml:id="echoid-s1594" xml:space="preserve">37636 paſſus ſuperficiales pro vnaqua-<lb/>que equitum regione, necnon & </s> <s xml:id="echoid-s1595" xml:space="preserve">pro ſuis plateis & </s> <s xml:id="echoid-s1596" xml:space="preserve">viis. <lb/></s> <s xml:id="echoid-s1597" xml:space="preserve">Præterea, ſi ſcire cupis quantum metiri debeas ad <lb/>oram viarum vt deſignentur foris regiones equitatus, <lb/>addentur 306 paſſus ſuperficiales, (pars ſcilicet plateæ <lb/>Imperatoris) cum paſſibus 1000 (dimidio videlicet <lb/>ſpatij quod occupant viri ſtrenui,) fient 1306. </s> <s xml:id="echoid-s1598" xml:space="preserve">ad quæ <lb/>addemus paſſus ſuperficiales 360, (pro via quæ ambit <lb/>dimidium ſpatij virorum ſtrenuorũ,) prodibunt 1666, <lb/>quibus adhuc addemus paſſus ſuperficiales 37636, <lb/>(ſpatium ſcilicet vnius equitum regionis) prodibunt <lb/>39302, à quibus radicem quadratam extrahemus, quæ <lb/>erit 198, & </s> <s xml:id="echoid-s1599" xml:space="preserve">paulo plus: </s> <s xml:id="echoid-s1600" xml:space="preserve">& </s> <s xml:id="echoid-s1601" xml:space="preserve">à 198 ſubtrahemus 36, (latus <lb/>videlicet quadrati dimidij ſpatij ſpatij quodinhabitant viri <lb/>ſtrenui, cum parte plateæ Imperatoris,) remanebunt <lb/>162, quos paſſus 162 dimetiemur ad viæ oram, initium <lb/>ſumentes à ſedibus virorum ſtrenuorum, & </s> <s xml:id="echoid-s1602" xml:space="preserve">à duabus <lb/>plateis mercatus & </s> <s xml:id="echoid-s1603" xml:space="preserve">macelli, relinquentes tamen ex his <lb/>162, paſſus 5 pro via quæ ambit dictas ſedes & </s> <s xml:id="echoid-s1604" xml:space="preserve">pla-<lb/>teas, formando regiones, cum ſuis plateis & </s> <s xml:id="echoid-s1605" xml:space="preserve">viis, vt in <lb/>figura apparet. </s> <s xml:id="echoid-s1606" xml:space="preserve">Quòd ſi quis ſcire vellet, quot paſſus <pb o="143" file="0143" n="172" rhead=""/> ſuperficiales ex iſtis quatuor regionibus occupant <lb/>equites leuis armaturæ, & </s> <s xml:id="echoid-s1607" xml:space="preserve">quot cataphracti, id hoc fiet <lb/>modo. </s> <s xml:id="echoid-s1608" xml:space="preserve">Iungentur vnà paſſus ſuperficiales cataphra-<lb/>ctorum, qui ſunt 28000, cum 80000, (qui equitatui <lb/>leuis armaturæ tributi ſunt,) prodibunt 108000. </s> <s xml:id="echoid-s1609" xml:space="preserve">Di-<lb/>uidentur deinde 108000 per 4, prodibunt 27000 paſ-<lb/>ſus ſuperficiales pro vnaquaque quatuor regionum. <lb/></s> <s xml:id="echoid-s1610" xml:space="preserve">Si autem indagare vis, quot, ex iſtis, cataphractis com-<lb/>petunt, quot equitibus leuis armaturæ, auferẽtur 27000 <lb/>à 28000, remanebunt 1000 paſſus ſuperficiales pro <lb/>cataphractis: </s> <s xml:id="echoid-s1611" xml:space="preserve">deinde auferes 1000 à 27000, remane-<lb/>bunt 26000 paſſus ſuperficiales, pro leuis armaturæ <lb/>equitibus: </s> <s xml:id="echoid-s1612" xml:space="preserve">ſicq́; </s> <s xml:id="echoid-s1613" xml:space="preserve">cataphracti ſibi vendicabunt regionem <lb/>vnam ex quatuor, cum parte alterius paſſuum ſuperfi-<lb/>cialium 1000: </s> <s xml:id="echoid-s1614" xml:space="preserve">equites leuis armaturæ duas cum alterius <lb/>parte paſſuum ſuperficialium 26000. </s> <s xml:id="echoid-s1615" xml:space="preserve">Itaque in vna <lb/>regione partim habitabunt cataphracti ad ſuperficia-<lb/>les paſſus 1000, partim equites leuis armaturæ ad paſ-<lb/>ſus ſuperficiales 26000. </s> <s xml:id="echoid-s1616" xml:space="preserve">Erunt autem equites leuis ar-<lb/>maturæ in vnaquaque duarum regionum 3375, in ter-<lb/>tia verò 3250 cum 72 cataphractis. </s> <s xml:id="echoid-s1617" xml:space="preserve">In quarta autem <lb/>regione habitabunt 1928 cataphracti. </s> <s xml:id="echoid-s1618" xml:space="preserve">Circa regiones <lb/>equitum ducetur vialata pedes decem, & </s> <s xml:id="echoid-s1619" xml:space="preserve">ad hanc viam <lb/>deſignabuntur regiones pro peditatu hoc modo: </s> <s xml:id="echoid-s1620" xml:space="preserve">Mul-<lb/>tiplicabimus pedites 48000, cum 64 pedibus ſuperfi-<lb/>cialibus ſoli, qui vnicuiq; </s> <s xml:id="echoid-s1621" xml:space="preserve">pediti tribuuntur, prodibunt <lb/>pedes ſuperficiales 3072000. </s> <s xml:id="echoid-s1622" xml:space="preserve">deinde multiplicabimus <lb/>pedes ſoli ſuperficiales 32, qui cuilibet pediti dãtur pro <lb/>armorum platea, cum peditibus 48000, fient pedes <lb/>ſuperficiales 1536000, quibus additis ad 3072000, pro <lb/>dibunt 4608000. </s> <s xml:id="echoid-s1623" xml:space="preserve">Hos pedes partiemur per 25, fient <pb o="144" file="0144" n="173" rhead=""/> 184320 paſſus ſuperficiales. </s> <s xml:id="echoid-s1624" xml:space="preserve">Præterea, hiſce 184320 <lb/>paſſibus addemus ſuperficiem plateæ munitionis bom <lb/>bardicæ, cui ſtatuimus dare in ſingula quatuor latera <lb/>paſſus 50, volumusq́; </s> <s xml:id="echoid-s1625" xml:space="preserve">eam ſegregatam eſſe ab omni <lb/>habitatione, ob incendiorum periculum. </s> <s xml:id="echoid-s1626" xml:space="preserve">Ducendo <lb/>igitur 50 in ſemet, fient 2500 paſſus ſuperficiales ſeu <lb/>quadrati, quibus additis ad 184320, fient 186820, <lb/>quibus in 4 diuiſis, prodibunt 46705 pro vnaquaque <lb/>quatuor regionum peditatus, cum plateis armorum <lb/>vnicuiq; </s> <s xml:id="echoid-s1627" xml:space="preserve">tributis, necnon & </s> <s xml:id="echoid-s1628" xml:space="preserve">pro platea munitionis <lb/>bombardicæ. </s> <s xml:id="echoid-s1629" xml:space="preserve">Verùm his regiombus addendæ ſunt <lb/>etiam ſuæ viæ. </s> <s xml:id="echoid-s1630" xml:space="preserve">Quod vt fiat, extrahemus radicem <lb/>quadratam è 46705, quæ fere erit 216: </s> <s xml:id="echoid-s1631" xml:space="preserve">quibus 216 <lb/>addemus paſſus 10 pro viarum latitudine, fient 226, <lb/>quæ 226 in ſe ducemus, ac prodibunt 51076 pro vna-<lb/>quaque peditatus regione, cum ſuis plateis & </s> <s xml:id="echoid-s1632" xml:space="preserve">viis. <lb/></s> <s xml:id="echoid-s1633" xml:space="preserve">Quòd ſiſcire velimus, quantum metiri debeamus ad <lb/>oram viarum præcipuarum, ad formandas regiones <lb/>peditatus: </s> <s xml:id="echoid-s1634" xml:space="preserve">initium ſumendo à via quæ ambit equitum <lb/>habitationes, hoc modo procedemus, ſimul jungendo <lb/>numeros ſequentes, ex iisq́; </s> <s xml:id="echoid-s1635" xml:space="preserve">vnicam ſummam facien-<lb/>tes. </s> <s xml:id="echoid-s1636" xml:space="preserve">Primò ad 51076 paſſus ſuperficiales regionis vnius <lb/>peditum, addemus paſſus 5000 pro via quæ ambit re-<lb/>gionem vnam equitum paſſus item ſuperfi-<lb/> <anchor type="note" xlink:label="note-0144-01a" xlink:href="note-0144-01"/> ciales 37636 regionis vnius equitum: </s> <s xml:id="echoid-s1637" xml:space="preserve">deinde <lb/>360 paſſus ſuperficiales pro via quæ ambit <lb/>partem vnam habitationis virorum ſtrenuo-<lb/>rum: </s> <s xml:id="echoid-s1638" xml:space="preserve">ad hæc paſſus ſuperficiales 1000 pro ſe-<lb/>de virorum ſtrenuorum: </s> <s xml:id="echoid-s1639" xml:space="preserve">præterea 306 paſſus <lb/>ſuperficiales pro parte plateæ Imperatoris. </s> <s xml:id="echoid-s1640" xml:space="preserve">His <lb/>omnibus ſimul junctis prodeunt paſſus ſu- <pb o="145" file="0145" n="174" rhead=""/> perficiales 95378, è quibus radicem quadratam extra-<lb/>hemus, quæ erit 309 paulo minus. </s> <s xml:id="echoid-s1641" xml:space="preserve">Ab his 309 aufe-<lb/>ro 198, remanebunt 111 paſſus, quos dimetiemur ad <lb/>oram viarum præcipuarũ, initium ſumendo à ſedibus <lb/>equitum leuis armaturæ: </s> <s xml:id="echoid-s1642" xml:space="preserve">detrahendo tamen priùs ab <lb/>illis 111, 10 paſſus pro latitudine viæ quæ ambit ſedes <lb/>equitum leuis armaturæ, deſignando regiones pedi-<lb/>tum cum platea commeatus bombardici, vt in noſtra <lb/>ichnographia apparet. </s> <s xml:id="echoid-s1643" xml:space="preserve">Eſt enim hæc platea bombar-<lb/>dica comprehenſa in ſupputatione regionum pedita-<lb/>tus. </s> <s xml:id="echoid-s1644" xml:space="preserve">Hanc autem bombardicam plateam, vellem abeſſe <lb/>à foſſis (tranchee) quæ circumdant caſtra, 40 vel 50 <lb/>paſſibus ad minus: </s> <s xml:id="echoid-s1645" xml:space="preserve">vt & </s> <s xml:id="echoid-s1646" xml:space="preserve">in noſtra ichnographia appa-<lb/>ret foſſas abeſſe à metatione 50 paſſibus. </s> <s xml:id="echoid-s1647" xml:space="preserve">Loca ne-<lb/>ceſſaria, quæ in ſingulis regionibus fiunt, ad requiſita <lb/>naturæ, tum militum, tum aliorum qui caſtra ſequun-<lb/>tur, fient ex eo quo minus abundant ſuperficies pla-<lb/>tearum armorum: </s> <s xml:id="echoid-s1648" xml:space="preserve">ſoli enim ſatis ſupérque à nobis da-<lb/>tum eſt illis plateis. </s> <s xml:id="echoid-s1649" xml:space="preserve">Ad formandas autem vias ipſa-<lb/>rum regionum, quæ ſeſe interſecent ad angulos rectos <lb/>in medio plateæ, addetur ad latus quadrati (ad radi-<lb/>cem ſcilicet quæ ſumitur ab vniuerſa ſuperficie regio-<lb/>nis) tantum quantum volumus regionis vias latas eſſe. <lb/></s> <s xml:id="echoid-s1650" xml:space="preserve">Huic noſtræ ichnographiæ addimus paſſus 10 pro lati <lb/>tudine earum viarum. </s> <s xml:id="echoid-s1651" xml:space="preserve">Hæc autẽ latitudo nullo modo <lb/>debet excedere oram latitudinis plateæ. </s> <s xml:id="echoid-s1652" xml:space="preserve">Hi verò paſſus <lb/>10 non ſolùm formant latitudinem viarum, ſed etiam <lb/>ampliant paſſibus 10 longitudinem & </s> <s xml:id="echoid-s1653" xml:space="preserve">latitudinem pla <lb/>tearũ armorum quæ in regionibus: </s> <s xml:id="echoid-s1654" xml:space="preserve">& </s> <s xml:id="echoid-s1655" xml:space="preserve">hoc quicquid eſt <lb/>li, quo hæ plateæ ampliantur, ſumetur pro locis neceſ-<lb/>ſariis, de quibus paulo ſuprà, vbi commodiùs videbi- <pb o="146" file="0146" n="175" rhead=""/> tur. </s> <s xml:id="echoid-s1656" xml:space="preserve">Pecora ad victum exercitus, cum foſſoribus, & </s> <s xml:id="echoid-s1657" xml:space="preserve"><lb/>aliis rebus nihili, deſignabuntur in humero vel cauda <lb/>metationis. </s> <s xml:id="echoid-s1658" xml:space="preserve">Macellarij tabernas ſuas habent in plateis <lb/>regionum & </s> <s xml:id="echoid-s1659" xml:space="preserve">ad oram præcipuarum viarum, vt ſuprà <lb/>dictum eſt. </s> <s xml:id="echoid-s1660" xml:space="preserve">Hæc autem omnia ex noſtris ichnogra-<lb/>phiis ſeu caſtrametationibus comprehẽdi poterunt: </s> <s xml:id="echoid-s1661" xml:space="preserve">in <lb/>quibus aduertat lector, vbicumque viderit litteram <emph style="sc">A</emph>, <lb/>deſignari per eam plateas regionum equitatus, pedita-<lb/>tus, & </s> <s xml:id="echoid-s1662" xml:space="preserve">Imperatoris, necnon & </s> <s xml:id="echoid-s1663" xml:space="preserve">vias, atque etiam ſpa-<lb/>tium illud, quod interjacet foſſas & </s> <s xml:id="echoid-s1664" xml:space="preserve">caſtrorum me-<lb/>tationem, Littera <emph style="sc">B</emph> indicat regiones equitum leuis ar-<lb/>maturæ. </s> <s xml:id="echoid-s1665" xml:space="preserve">Littera <emph style="sc">C</emph> regiones cataphractorum. </s> <s xml:id="echoid-s1666" xml:space="preserve">Littera <lb/><emph style="sc">D</emph> regiones peditatus. </s> <s xml:id="echoid-s1667" xml:space="preserve">Littera <emph style="sc">E</emph> plateam commeatus <lb/>bombardici. </s> <s xml:id="echoid-s1668" xml:space="preserve">Littera <emph style="sc">F</emph>, viros ſtrenuos ſeu inſignes, qui <lb/>Imperatori adſtant. </s> <s xml:id="echoid-s1669" xml:space="preserve">Littera <emph style="sc">G</emph> plateam mercatus. </s> <s xml:id="echoid-s1670" xml:space="preserve">Lit-<lb/>tera <emph style="sc">H</emph> plateam macelli. </s> <s xml:id="echoid-s1671" xml:space="preserve">Littera <emph style="sc">I</emph> loca vbiſunt foſſores, <lb/>& </s> <s xml:id="echoid-s1672" xml:space="preserve">pecora quæ ad exercitus victum mactantur, <lb/>aliæq́; </s> <s xml:id="echoid-s1673" xml:space="preserve">res inutiles. </s> <s xml:id="echoid-s1674" xml:space="preserve">Littera <emph style="sc">K</emph> vallum ſeu <lb/>aggerem ſuper colle, ad tuitio-<lb/>nem caſtrorum.</s> <s xml:id="echoid-s1675" xml:space="preserve"/> </p> <div xml:id="echoid-div45" type="float" level="2" n="1"> <note position="right" xlink:label="note-0144-01" xlink:href="note-0144-01a" xml:space="preserve"> <lb/>51076 <lb/>5000 <lb/>37636 <lb/>360 <lb/>1000 <lb/>306 <lb/>95378 <lb/></note> </div> <figure> <image file="0146-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0146-01"/> </figure> </div> <div xml:id="echoid-div47" type="section" level="1" n="38"> <head xml:id="echoid-head47" xml:space="preserve">HIC DEBENT INSERI DVO</head> <head xml:id="echoid-head48" style="it" xml:space="preserve">castrametationum folia.</head> <pb o="146" file="0146a" n="176" rhead=""/> <figure> <image file="0146a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0146a-01"/> </figure> <pb o="146" file="0146b" n="177" rhead=""/> <figure> <image file="0146b-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0146b-01"/> </figure> <pb o="146" file="0164c" n="178" rhead=""/> <figure> <image file="0164c-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0164c-01"/> </figure> <pb o="147" file="0147" n="179" rhead=""/> <p> <s xml:id="echoid-s1676" xml:space="preserve">Hæc caſtrametationis ſupputatio viam docebit <lb/>qua poſſint pleræque aliæ ſupputari, ſiue varient in ſi-<lb/>tu, ſiue in numero militum, ſiue in vtroque, modò <lb/>exactè obſeruentur menſuræ debitæ. </s> <s xml:id="echoid-s1677" xml:space="preserve">Quòd ſi quis <lb/>mente teneat ea quæ à nobis ſuprà dicta ſunt, is facilè <lb/>& </s> <s xml:id="echoid-s1678" xml:space="preserve">citò poterit deſignare quaſuis caſtrorum metatio-<lb/>nes, cum ſuis menſuris, tum regionum, tum platea-<lb/>rum, viarum, & </s> <s xml:id="echoid-s1679" xml:space="preserve">aliarum rerum in caſtris neceſſariarum, <lb/>ac in quouis ſitu caſtra metanda ſint. </s> <s xml:id="echoid-s1680" xml:space="preserve">Attentè ergo le-<lb/>gat & </s> <s xml:id="echoid-s1681" xml:space="preserve">diſcat lector ea quæ à nobis ſcripta & </s> <s xml:id="echoid-s1682" xml:space="preserve">deſignata <lb/>ſunt.</s> <s xml:id="echoid-s1683" xml:space="preserve"/> </p> <figure> <image file="0147-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0147-01"/> </figure> </div> <div xml:id="echoid-div48" type="section" level="1" n="39"> <head xml:id="echoid-head49" xml:space="preserve">De profectione ſeu migratione exer <lb/>citus, qui ab hoſtili acie abſcedere <lb/>vult.</head> <head xml:id="echoid-head50" xml:space="preserve">CAPVT NONVM.</head> <p> <s xml:id="echoid-s1684" xml:space="preserve"><emph style="sc">QVvm</emph> ſeſe comitentur profectio & </s> <s xml:id="echoid-s1685" xml:space="preserve">me-<lb/>tatio exercituum, dicam quàm paucis po-<lb/>tero, id quod mihi ère videbitur, quodq́; <lb/></s> <s xml:id="echoid-s1686" xml:space="preserve">factitatum eſt in bellis hujuſce noſtri <lb/>æui, circa migrationem exercitus, ſta-<lb/>tuentes tamen duos hoſtiles exercitus ſibi inuicem im-<lb/>minere, vel alterum ab altero parum abeſſe. </s> <s xml:id="echoid-s1687" xml:space="preserve">Quia <lb/>verò res eſt magni momenti, gnarum eſſe omnium <lb/>carum operationum quæ cadunt in ducem, ſeu virum <pb o="148" file="0148" n="180" rhead=""/> qui bella tractat, in hoc argumento certè multæ etiam <lb/>conſiderationes requiruntur. </s> <s xml:id="echoid-s1688" xml:space="preserve">Migrare noctu, & </s> <s xml:id="echoid-s1689" xml:space="preserve">abſce-<lb/>dere ab hoſte, cenſetur quidem tutius remedium <lb/>quàm quoduis aliud: </s> <s xml:id="echoid-s1690" xml:space="preserve">attamen non mihi videtur hoc <lb/>ſatis eſſe, quo quis poſſit voti ſui compos fieri, ſi is, <lb/>qui migrare vult, non juuetur à ſitu & </s> <s xml:id="echoid-s1691" xml:space="preserve">aliis qualitati-<lb/>bus regionis in quam migrare cupit. </s> <s xml:id="echoid-s1692" xml:space="preserve">Sed hæc ſigil-<lb/>latim examinando, dico, quando noctu proficiſcimur, <lb/>debere nos ſumma diligentia vti: </s> <s xml:id="echoid-s1693" xml:space="preserve">neque hæc diligentia <lb/>ſufficiens eſſe poteſt, niſi ſitu juuetur. </s> <s xml:id="echoid-s1694" xml:space="preserve">Si quis enim <lb/>per planities & </s> <s xml:id="echoid-s1695" xml:space="preserve">loca patentia iter habeat, neque illi ſit, <lb/>vbi hoſtis de ipſius abitu reſciuerit, vel ſylua vel vallis <lb/>quæ ſuos recipiat, difficillimè, vt dixi, poterit ſe ſuosq́; <lb/></s> <s xml:id="echoid-s1696" xml:space="preserve">tueri, quidquid agat, quidquid moueat: </s> <s xml:id="echoid-s1697" xml:space="preserve">quia equita-<lb/>tus hoſtilis ſuperueniens, illum facilè remorabitur, <lb/>cogetq́; </s> <s xml:id="echoid-s1698" xml:space="preserve">vel inuitũ manus conſerere, idq́; </s> <s xml:id="echoid-s1699" xml:space="preserve">confuſo exer-<lb/>citu, quum illi tempus ab hoſte non detur aciem in-<lb/>ſtruendi: </s> <s xml:id="echoid-s1700" xml:space="preserve">habeatq́; </s> <s xml:id="echoid-s1701" xml:space="preserve">ſecum bombardas, & </s> <s xml:id="echoid-s1702" xml:space="preserve">alia exercitus <lb/>impedimenta, quæ non æquum eſt in prædam hoſti <lb/>relinquere. </s> <s xml:id="echoid-s1703" xml:space="preserve">Non decet etiam cogere milites, vt paſſu ci-<lb/>tatiore progrediantur, quàm ſoliti ſint: </s> <s xml:id="echoid-s1704" xml:space="preserve">ex hac enim co-<lb/>actione in animos militũ ſerperet ſiniſtra opinio præ-<lb/>ter eam quam jam imbiberũt ob talem migrationem. </s> <s xml:id="echoid-s1705" xml:space="preserve"><lb/>Res proculdubiò magni periculi, & </s> <s xml:id="echoid-s1706" xml:space="preserve">ex qua confuſio <lb/>immedicabilis naſceretur, vt ſæpiſſimè accidit. </s> <s xml:id="echoid-s1707" xml:space="preserve">Exerci-<lb/>tus hoſtilis, fugientes inſequens, in has anguſtias non <lb/>cadit. </s> <s xml:id="echoid-s1708" xml:space="preserve">Liberè enim poteſt impedimenta omnia dere-<lb/>linquere. </s> <s xml:id="echoid-s1709" xml:space="preserve">Quinimmo, ſi gradum acceleret, id multò <lb/>animoſiores ſuos reddet, præcipuè vbi accelerationem <lb/>iſtam dux ornabit magnificis illis & </s> <s xml:id="echoid-s1710" xml:space="preserve">ampullatis verbis, <lb/>quæ in ſimili caſu conueniunt. </s> <s xml:id="echoid-s1711" xml:space="preserve">Quidquid ſit, arbi- <pb o="149" file="0149" n="181" rhead=""/> tror migrationem illam nocturnam vndequaq; </s> <s xml:id="echoid-s1712" xml:space="preserve">tutam <lb/>non eſſe, ni ſitus loci eam comitetur, quemadmodum <lb/>accidit Franciſco Galliarum Regi, de quo ſuprà, quan-<lb/>do ad Cambreſium abſceſſit ab Imperatore tempore <lb/>nocturno, vbi, magnæ ſyluæ beneficio, immunem <lb/>periculi reddidit exercitum ſuum: </s> <s xml:id="echoid-s1713" xml:space="preserve">ſyluam enim illam <lb/>præterierat, antequam ad eum eſſet hoſtilis equitatus. <lb/></s> <s xml:id="echoid-s1714" xml:space="preserve">Tunc gradum ſtitit, paratus prælio decernere, ſeu be-<lb/>neficio ſyluæ, ſeu loci commoditate illectus. </s> <s xml:id="echoid-s1715" xml:space="preserve">Non ita <lb/>ceſſit imperiali exercitui. </s> <s xml:id="echoid-s1716" xml:space="preserve">Dum enim incogitantiùs <lb/>hoſtem perſequuntur, ſylua præterita, exercitum re-<lb/>gium paratum repererunt, vnde major pars eorum vel <lb/>cæſi, vel capti. </s> <s xml:id="echoid-s1717" xml:space="preserve">Idem ferè accidit in Germania. </s> <s xml:id="echoid-s1718" xml:space="preserve">Quum <lb/>enim Proteſtantes retrocedere vellent, & </s> <s xml:id="echoid-s1719" xml:space="preserve">abſcedere ab <lb/>Imperiali exercitu qui illis in faucibus erat, de nocte iti-<lb/>dem migrantes, non longè progreſſi ſunt, quin in mu-<lb/>nitiſſimam vallem ingrederentur, in qua niſi cum ma-<lb/>ximo incommodo poterat in eos hoſtis impetum fa-<lb/>cere. </s> <s xml:id="echoid-s1720" xml:space="preserve">Collis namque, qui in ipſo vallis introitu erat, <lb/>ſubitò à Proteſtantibus occupatus eſt, & </s> <s xml:id="echoid-s1721" xml:space="preserve">munitus bo-<lb/>nis bombardis campeſtribus, necnon & </s> <s xml:id="echoid-s1722" xml:space="preserve">magna copia <lb/>equitatus & </s> <s xml:id="echoid-s1723" xml:space="preserve">peditatus. </s> <s xml:id="echoid-s1724" xml:space="preserve">Præterea ſylua proxima ſclope-<lb/>tariis repleta ab eis ſuit, ſic vt exercitus imperialis nequi <lb/>uerit eos ampliùs proſequi, vt conſtituerat. </s> <s xml:id="echoid-s1725" xml:space="preserve">Quũ enim <lb/>proximèacceſſiſſet, agnouiſſetq́; </s> <s xml:id="echoid-s1726" xml:space="preserve">in locum arte & </s> <s xml:id="echoid-s1727" xml:space="preserve">natu-<lb/>ra tutiſſimum eos ſeceſſiſſe, deſtitit ampliùs inſequi. </s> <s xml:id="echoid-s1728" xml:space="preserve"><lb/>Dico igitur, fauore ſitus & </s> <s xml:id="echoid-s1729" xml:space="preserve">regionum, tutum reddi poſ-<lb/>ſe receptum, vt ex ſuprà dictis exemplis apparet. </s> <s xml:id="echoid-s1730" xml:space="preserve">Atta-<lb/>men non nego multo tutiorem eſſe migrationem no-<lb/>cturnam, vt ſaltem poſſimus tantum itineris lucrari, <lb/>quod ſatis ſit ad appellendum ad locum munitum:</s> <s xml:id="echoid-s1731" xml:space="preserve"> <pb o="150" file="0150" n="182" rhead=""/> quia receptus interdiu factus, abſque ſitus ſecuritate, <lb/>majori ex parte periculoſus eſt, niſi is, qui ſecedat, equi-<lb/>tatu ſuperior ſit. </s> <s xml:id="echoid-s1732" xml:space="preserve">Qui autem inferior eſt, is quantum <lb/>poteſt, debet ab hoſte abeſſe, ne, ob ea, quæ <lb/>ſuprà dicta ſunt, cogatur in aliquam <lb/>inſignem confuſionem <lb/>deſcendere.</s> <s xml:id="echoid-s1733" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div49" type="section" level="1" n="40"> <head xml:id="echoid-head51" xml:space="preserve">FINIS.</head> <figure> <image file="0150-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0150-01"/> </figure> <pb file="0151" n="183"/> <figure> <image file="0151-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0151-01"/> </figure> </div> <div xml:id="echoid-div50" type="section" level="1" n="41"> <head xml:id="echoid-head52" xml:space="preserve">CAPITVM SERIES</head> <p style="it"> <s xml:id="echoid-s1734" xml:space="preserve">Geometricæ quædam operationes, quæ faciunt ad arcium ſeu <lb/>propugnaculorum fabricam. </s> <s xml:id="echoid-s1735" xml:space="preserve">_CAP. </s> <s xml:id="echoid-s1736" xml:space="preserve">I._ </s> <s xml:id="echoid-s1737" xml:space="preserve">pag. </s> <s xml:id="echoid-s1738" xml:space="preserve">1</s> </p> <p style="it"> <s xml:id="echoid-s1739" xml:space="preserve">Quomodo poßint deſignari arces ſeu propugnacula, cum eorum <lb/>menſuris, aliìsque rebus quæ ſibi competunt. </s> <s xml:id="echoid-s1740" xml:space="preserve">_C. </s> <s xml:id="echoid-s1741" xml:space="preserve">II. </s> <s xml:id="echoid-s1742" xml:space="preserve">26_</s> </p> <p style="it"> <s xml:id="echoid-s1743" xml:space="preserve">Quid conſiderandum ſit ei, qui à Principe ſuo electus eſt ad de-<lb/>fenſionem ſeu propugnationem arcis alicujus. </s> <s xml:id="echoid-s1744" xml:space="preserve">_C. </s> <s xml:id="echoid-s1745" xml:space="preserve">III. </s> <s xml:id="echoid-s1746" xml:space="preserve">95_</s> </p> <p style="it"> <s xml:id="echoid-s1747" xml:space="preserve">De modo cuctodiendi ac conſeruandi arces. </s> <s xml:id="echoid-s1748" xml:space="preserve">_C. </s> <s xml:id="echoid-s1749" xml:space="preserve">IIII. </s> <s xml:id="echoid-s1750" xml:space="preserve">97_</s> </p> <p style="it"> <s xml:id="echoid-s1751" xml:space="preserve">Quo pacto ſe gerat Imperator, qui viderit arcem aliquam expu-<lb/>gnari non poſſe: </s> <s xml:id="echoid-s1752" xml:space="preserve">ac quomodo eam ſit obſeſſurus. </s> <s xml:id="echoid-s1753" xml:space="preserve">_C. </s> <s xml:id="echoid-s1754" xml:space="preserve">V. </s> <s xml:id="echoid-s1755" xml:space="preserve">101_</s> </p> <p style="it"> <s xml:id="echoid-s1756" xml:space="preserve">Quomodo ſe geret Imperator, vbi viderit arcem expugnari poſ-<lb/>ſe. </s> <s xml:id="echoid-s1757" xml:space="preserve">_C. </s> <s xml:id="echoid-s1758" xml:space="preserve">VI. </s> <s xml:id="echoid-s1759" xml:space="preserve">105_</s> </p> <p style="it"> <s xml:id="echoid-s1760" xml:space="preserve">Quo pacto ſe gerere debeant propugnatores, & </s> <s xml:id="echoid-s1761" xml:space="preserve">quibus remedijs <lb/>vti poßint. </s> <s xml:id="echoid-s1762" xml:space="preserve">_C. </s> <s xml:id="echoid-s1763" xml:space="preserve">VII. </s> <s xml:id="echoid-s1764" xml:space="preserve">114_</s> </p> <p style="it"> <s xml:id="echoid-s1765" xml:space="preserve">Exercitus, ſiue aciei, itinera, castrorum metationes: </s> <s xml:id="echoid-s1766" xml:space="preserve">& </s> <s xml:id="echoid-s1767" xml:space="preserve">quo-<lb/>modo eæ metationes fieri debeant. </s> <s xml:id="echoid-s1768" xml:space="preserve">_C. </s> <s xml:id="echoid-s1769" xml:space="preserve">VIII. </s> <s xml:id="echoid-s1770" xml:space="preserve">133_</s> </p> <p style="it"> <s xml:id="echoid-s1771" xml:space="preserve">De profectione ſeu migratione exercitus, qui ab hostili acie abſ-<lb/>cedere vult. </s> <s xml:id="echoid-s1772" xml:space="preserve">_C. </s> <s xml:id="echoid-s1773" xml:space="preserve">IX. </s> <s xml:id="echoid-s1774" xml:space="preserve">147_</s> </p> <figure> <image file="0151-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0151-02"/> </figure> <pb file="0152" n="184"/> <figure> <image file="0152-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0152-01"/> </figure> </div> </text> </echo>